TSTP Solution File: SWV421-1.105 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV421-1.105 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 15:12:00 EDT 2022
% Result : Unsatisfiable 0.85s 0.83s
% Output : Proof 2.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV421-1.105 : TPTP v8.1.0. Released v3.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 03:12:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.85/0.83 % SZS status Unsatisfiable
% 0.85/0.83 % SZS output start Proof
% 0.85/0.83 tff(node14_type, type, (
% 0.85/0.83 node14: ( $i * $i ) > $o)).
% 0.85/0.83 tff(s103_type, type, (
% 0.85/0.83 s103: $i)).
% 0.85/0.83 tff(s104_type, type, (
% 0.85/0.83 s104: $i)).
% 0.85/0.83 tff(trans_type, type, (
% 0.85/0.83 trans: ( $i * $i ) > $o)).
% 0.85/0.83 tff(s38_type, type, (
% 0.85/0.83 s38: $i)).
% 0.85/0.83 tff(always19_type, type, (
% 0.85/0.83 always19: $i > $o)).
% 0.85/0.83 tff(m_main_v_state1_type, type, (
% 0.85/0.83 m_main_v_state1: ( $i * $i ) > $o)).
% 0.85/0.83 tff(c_c1_type, type, (
% 0.85/0.83 c_c1: $i)).
% 0.85/0.83 tff(node3_type, type, (
% 0.85/0.83 node3: $i > $o)).
% 0.85/0.83 tff(s37_type, type, (
% 0.85/0.83 s37: $i)).
% 0.85/0.83 tff(m_main_v_state2_type, type, (
% 0.85/0.83 m_main_v_state2: ( $i * $i ) > $o)).
% 0.85/0.83 tff(c_c2_type, type, (
% 0.85/0.83 c_c2: $i)).
% 0.85/0.83 tff(c_n2_type, type, (
% 0.85/0.83 c_n2: $i)).
% 0.85/0.83 tff(node12_type, type, (
% 0.85/0.83 node12: $i > $o)).
% 0.85/0.83 tff(s36_type, type, (
% 0.85/0.83 s36: $i)).
% 0.85/0.83 tff(c_t2_type, type, (
% 0.85/0.83 c_t2: $i)).
% 0.85/0.83 tff(node9_type, type, (
% 0.85/0.83 node9: $i > $o)).
% 0.85/0.83 tff(s35_type, type, (
% 0.85/0.83 s35: $i)).
% 0.85/0.83 tff(node13_type, type, (
% 0.85/0.83 node13: ( $i * $i ) > $o)).
% 0.85/0.83 tff(s34_type, type, (
% 0.85/0.83 s34: $i)).
% 0.85/0.83 tff(m_main_v_turn_type, type, (
% 0.85/0.83 m_main_v_turn: ( $i * $i ) > $o)).
% 0.85/0.83 tff(c_2_type, type, (
% 0.85/0.83 c_2: $i)).
% 0.85/0.83 tff(c_1_type, type, (
% 0.85/0.83 c_1: $i)).
% 0.85/0.83 tff(c_t1_type, type, (
% 0.85/0.83 c_t1: $i)).
% 0.85/0.83 tff(s33_type, type, (
% 0.85/0.83 s33: $i)).
% 0.85/0.83 tff(node6_type, type, (
% 0.85/0.83 node6: ( $i * $i ) > $o)).
% 0.85/0.83 tff(s32_type, type, (
% 0.85/0.83 s32: $i)).
% 0.85/0.83 tff(node1_type, type, (
% 0.85/0.83 node1: $i > $o)).
% 0.85/0.83 tff(c_n1_type, type, (
% 0.85/0.83 c_n1: $i)).
% 0.85/0.83 tff(s31_type, type, (
% 0.85/0.83 s31: $i)).
% 0.85/0.83 tff(node5_type, type, (
% 0.85/0.83 node5: $i > $o)).
% 0.85/0.83 tff(s30_type, type, (
% 0.85/0.83 s30: $i)).
% 0.85/0.83 tff(s29_type, type, (
% 0.85/0.83 s29: $i)).
% 0.85/0.83 tff(s28_type, type, (
% 0.85/0.83 s28: $i)).
% 0.85/0.83 tff(s27_type, type, (
% 0.85/0.83 s27: $i)).
% 0.85/0.83 tff(s26_type, type, (
% 0.85/0.83 s26: $i)).
% 0.85/0.83 tff(s25_type, type, (
% 0.85/0.83 s25: $i)).
% 0.85/0.83 tff(s24_type, type, (
% 0.85/0.83 s24: $i)).
% 0.85/0.83 tff(s23_type, type, (
% 0.85/0.83 s23: $i)).
% 0.85/0.83 tff(s22_type, type, (
% 0.85/0.83 s22: $i)).
% 0.85/0.83 tff(s21_type, type, (
% 0.85/0.83 s21: $i)).
% 0.85/0.83 tff(s20_type, type, (
% 0.85/0.83 s20: $i)).
% 0.85/0.83 tff(s19_type, type, (
% 0.85/0.83 s19: $i)).
% 0.85/0.83 tff(s18_type, type, (
% 0.85/0.83 s18: $i)).
% 0.85/0.83 tff(s17_type, type, (
% 0.85/0.83 s17: $i)).
% 0.85/0.83 tff(s16_type, type, (
% 0.85/0.83 s16: $i)).
% 0.85/0.83 tff(s15_type, type, (
% 0.85/0.83 s15: $i)).
% 0.85/0.83 tff(s14_type, type, (
% 0.85/0.83 s14: $i)).
% 0.85/0.83 tff(s13_type, type, (
% 0.85/0.83 s13: $i)).
% 0.85/0.83 tff(s12_type, type, (
% 0.85/0.83 s12: $i)).
% 0.85/0.83 tff(s11_type, type, (
% 0.85/0.83 s11: $i)).
% 0.85/0.83 tff(s10_type, type, (
% 0.85/0.83 s10: $i)).
% 0.85/0.83 tff(s9_type, type, (
% 0.85/0.83 s9: $i)).
% 0.85/0.83 tff(s8_type, type, (
% 0.85/0.83 s8: $i)).
% 0.85/0.83 tff(s7_type, type, (
% 0.85/0.83 s7: $i)).
% 0.85/0.83 tff(s6_type, type, (
% 0.85/0.83 s6: $i)).
% 0.85/0.83 tff(s5_type, type, (
% 0.85/0.83 s5: $i)).
% 0.85/0.83 tff(s4_type, type, (
% 0.85/0.83 s4: $i)).
% 0.85/0.83 tff(s3_type, type, (
% 0.85/0.83 s3: $i)).
% 0.85/0.83 tff(s2_type, type, (
% 0.85/0.83 s2: $i)).
% 0.85/0.83 tff(s1_type, type, (
% 0.85/0.83 s1: $i)).
% 0.85/0.83 tff(node8_type, type, (
% 0.85/0.83 node8: $i > $o)).
% 0.85/0.83 tff(s0_type, type, (
% 0.85/0.83 s0: $i)).
% 0.85/0.83 tff(succ_type, type, (
% 0.85/0.83 succ: ( $i * $i ) > $o)).
% 0.85/0.83 tff(node17_type, type, (
% 0.85/0.83 node17: ( $i * $i ) > $o)).
% 0.85/0.83 tff(node15_type, type, (
% 0.85/0.83 node15: $i > $o)).
% 0.85/0.83 tff(node16_type, type, (
% 0.85/0.83 node16: $i > $o)).
% 0.85/0.83 tff(node18_type, type, (
% 0.85/0.83 node18: ( $i * $i ) > $o)).
% 0.85/0.83 tff(node11_type, type, (
% 0.85/0.83 node11: $i > $o)).
% 0.85/0.83 tff(node7_type, type, (
% 0.85/0.83 node7: ( $i * $i ) > $o)).
% 0.85/0.83 tff(node10_type, type, (
% 0.85/0.83 node10: $i > $o)).
% 0.85/0.83 tff(node4_type, type, (
% 0.85/0.83 node4: $i > $o)).
% 0.85/0.83 tff(node2_type, type, (
% 0.85/0.83 node2: $i > $o)).
% 0.85/0.83 tff(node20_type, type, (
% 0.85/0.83 node20: $i > $o)).
% 0.85/0.83 tff(xuntil22_type, type, (
% 0.85/0.83 xuntil22: $i > $o)).
% 0.85/0.83 tff(until21_type, type, (
% 0.85/0.83 until21: $i > $o)).
% 0.85/0.83 tff(s102_type, type, (
% 0.85/0.83 s102: $i)).
% 0.85/0.83 tff(s101_type, type, (
% 0.85/0.83 s101: $i)).
% 0.85/0.83 tff(s100_type, type, (
% 0.85/0.83 s100: $i)).
% 0.85/0.83 tff(s99_type, type, (
% 0.85/0.83 s99: $i)).
% 0.85/0.83 tff(s98_type, type, (
% 0.85/0.83 s98: $i)).
% 0.85/0.83 tff(s97_type, type, (
% 0.85/0.83 s97: $i)).
% 0.85/0.83 tff(s96_type, type, (
% 0.85/0.83 s96: $i)).
% 0.85/0.83 tff(s95_type, type, (
% 0.85/0.83 s95: $i)).
% 0.85/0.83 tff(s94_type, type, (
% 0.85/0.83 s94: $i)).
% 0.85/0.83 tff(s93_type, type, (
% 0.85/0.83 s93: $i)).
% 0.85/0.83 tff(s92_type, type, (
% 0.85/0.83 s92: $i)).
% 0.85/0.83 tff(s91_type, type, (
% 0.85/0.83 s91: $i)).
% 0.85/0.83 tff(s90_type, type, (
% 0.85/0.83 s90: $i)).
% 0.85/0.83 tff(s89_type, type, (
% 0.85/0.83 s89: $i)).
% 0.85/0.83 tff(s88_type, type, (
% 0.85/0.83 s88: $i)).
% 0.85/0.83 tff(s87_type, type, (
% 0.85/0.83 s87: $i)).
% 0.85/0.83 tff(s86_type, type, (
% 0.85/0.83 s86: $i)).
% 0.85/0.83 tff(s85_type, type, (
% 0.85/0.83 s85: $i)).
% 0.85/0.83 tff(s84_type, type, (
% 0.85/0.83 s84: $i)).
% 0.85/0.83 tff(s83_type, type, (
% 0.85/0.83 s83: $i)).
% 0.85/0.83 tff(s82_type, type, (
% 0.85/0.83 s82: $i)).
% 0.85/0.83 tff(s81_type, type, (
% 0.85/0.83 s81: $i)).
% 0.85/0.83 tff(s80_type, type, (
% 0.85/0.83 s80: $i)).
% 0.85/0.83 tff(s79_type, type, (
% 0.85/0.83 s79: $i)).
% 0.85/0.83 tff(s78_type, type, (
% 0.85/0.83 s78: $i)).
% 0.85/0.83 tff(s77_type, type, (
% 0.85/0.83 s77: $i)).
% 0.85/0.83 tff(s76_type, type, (
% 0.85/0.83 s76: $i)).
% 0.85/0.83 tff(s75_type, type, (
% 0.85/0.83 s75: $i)).
% 0.85/0.83 tff(s74_type, type, (
% 0.85/0.83 s74: $i)).
% 0.85/0.83 tff(s73_type, type, (
% 0.85/0.83 s73: $i)).
% 0.85/0.83 tff(s72_type, type, (
% 0.85/0.83 s72: $i)).
% 0.85/0.83 tff(s71_type, type, (
% 0.85/0.83 s71: $i)).
% 0.85/0.83 tff(s70_type, type, (
% 0.85/0.83 s70: $i)).
% 0.85/0.83 tff(s69_type, type, (
% 0.85/0.83 s69: $i)).
% 0.85/0.83 tff(s68_type, type, (
% 0.85/0.83 s68: $i)).
% 0.85/0.83 tff(s67_type, type, (
% 0.85/0.83 s67: $i)).
% 0.85/0.83 tff(s66_type, type, (
% 0.85/0.83 s66: $i)).
% 0.85/0.83 tff(s65_type, type, (
% 0.85/0.83 s65: $i)).
% 0.85/0.83 tff(s64_type, type, (
% 0.85/0.83 s64: $i)).
% 0.85/0.83 tff(s63_type, type, (
% 0.85/0.83 s63: $i)).
% 0.85/0.83 tff(s62_type, type, (
% 0.85/0.83 s62: $i)).
% 0.85/0.83 tff(s61_type, type, (
% 0.85/0.83 s61: $i)).
% 0.85/0.83 tff(s60_type, type, (
% 0.85/0.83 s60: $i)).
% 0.85/0.83 tff(s59_type, type, (
% 0.85/0.83 s59: $i)).
% 0.85/0.83 tff(s58_type, type, (
% 0.85/0.83 s58: $i)).
% 0.85/0.83 tff(s57_type, type, (
% 0.85/0.83 s57: $i)).
% 0.85/0.83 tff(s56_type, type, (
% 0.85/0.83 s56: $i)).
% 0.85/0.83 tff(s55_type, type, (
% 0.85/0.83 s55: $i)).
% 0.85/0.83 tff(s54_type, type, (
% 0.85/0.83 s54: $i)).
% 0.85/0.83 tff(s53_type, type, (
% 0.85/0.83 s53: $i)).
% 0.85/0.83 tff(s52_type, type, (
% 0.85/0.83 s52: $i)).
% 0.85/0.83 tff(s51_type, type, (
% 0.85/0.83 s51: $i)).
% 0.85/0.83 tff(s50_type, type, (
% 0.85/0.83 s50: $i)).
% 0.85/0.83 tff(s49_type, type, (
% 0.85/0.83 s49: $i)).
% 0.85/0.83 tff(s48_type, type, (
% 0.85/0.83 s48: $i)).
% 0.85/0.83 tff(s47_type, type, (
% 0.85/0.83 s47: $i)).
% 0.85/0.83 tff(s46_type, type, (
% 0.85/0.83 s46: $i)).
% 0.85/0.83 tff(s45_type, type, (
% 0.85/0.83 s45: $i)).
% 0.85/0.83 tff(s44_type, type, (
% 0.85/0.83 s44: $i)).
% 0.85/0.83 tff(s43_type, type, (
% 0.85/0.83 s43: $i)).
% 0.85/0.83 tff(s42_type, type, (
% 0.85/0.83 s42: $i)).
% 0.85/0.83 tff(s41_type, type, (
% 0.85/0.83 s41: $i)).
% 0.85/0.83 tff(s40_type, type, (
% 0.85/0.83 s40: $i)).
% 0.85/0.83 tff(s39_type, type, (
% 0.85/0.83 s39: $i)).
% 0.85/0.83 tff(until2p23_type, type, (
% 0.85/0.83 until2p23: $i > $o)).
% 0.85/0.83 tff(xuntil2p24_type, type, (
% 0.85/0.83 xuntil2p24: $i > $o)).
% 0.85/0.83 tff(last_type, type, (
% 0.85/0.83 last: $i > $o)).
% 0.85/0.83 tff(loop_type, type, (
% 0.85/0.83 loop: $o)).
% 0.85/0.83 tff(1,plain,
% 0.85/0.83 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node14(X, Y)) <=> ((~trans(X, Y)) | node14(X, Y)))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(2,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[1])).
% 0.85/0.83 tff(3,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(4,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_55')).
% 0.85/0.83 tff(5,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.85/0.83 tff(6,plain,(
% 0.85/0.83 ![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.85/0.83 inference(skolemize,[status(sab)],[5])).
% 0.85/0.83 tff(7,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.85/0.83 tff(8,plain,
% 0.85/0.83 (m_main_v_state1(s0, c_n1) <=> m_main_v_state1(s0, c_n1)),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(9,axiom,(m_main_v_state1(s0, c_n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_11')).
% 0.85/0.83 tff(10,plain,
% 0.85/0.83 (m_main_v_state1(s0, c_n1)),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.85/0.83 tff(11,plain,
% 0.85/0.83 (^[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))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(12,plain,
% 0.85/0.83 (![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)))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[11])).
% 0.85/0.83 tff(13,plain,
% 0.85/0.83 (![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)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(14,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')).
% 0.85/0.83 tff(15,plain,
% 0.85/0.83 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.85/0.83 tff(16,plain,(
% 0.85/0.83 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.85/0.83 inference(skolemize,[status(sab)],[15])).
% 0.85/0.83 tff(17,plain,
% 0.85/0.83 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.85/0.83 tff(18,plain,
% 0.85/0.83 (((~![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)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(19,plain,
% 0.85/0.83 ((~![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)))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(20,plain,
% 0.85/0.83 ((~![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))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.85/0.83 tff(21,plain,
% 0.85/0.83 (~m_main_v_state1(s0, c_t1)),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.85/0.83 tff(22,plain,
% 0.85/0.83 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node8(X))) <=> (m_main_v_state1(X, c_t1) | (~node8(X))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(23,plain,
% 0.85/0.83 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[22])).
% 0.85/0.83 tff(24,plain,
% 0.85/0.83 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(25,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_36')).
% 0.85/0.83 tff(26,plain,
% 0.85/0.83 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.85/0.83 tff(27,plain,(
% 0.85/0.83 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.85/0.83 inference(skolemize,[status(sab)],[26])).
% 0.85/0.83 tff(28,plain,
% 0.85/0.83 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.85/0.83 tff(29,plain,
% 0.85/0.83 (((~![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)))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(30,plain,
% 0.85/0.83 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | (m_main_v_state1(s0, c_t1) | (~node8(s0)))),
% 0.85/0.83 inference(quant_inst,[status(thm)],[])).
% 0.85/0.83 tff(31,plain,
% 0.85/0.83 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node8(X)))) | m_main_v_state1(s0, c_t1) | (~node8(s0))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.85/0.83 tff(32,plain,
% 0.85/0.83 (~node8(s0)),
% 0.85/0.83 inference(unit_resolution,[status(thm)],[31, 28, 21])).
% 0.85/0.83 tff(33,plain,
% 0.85/0.83 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(34,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[33])).
% 0.85/0.83 tff(35,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(36,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound106')).
% 0.85/0.83 tff(37,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.85/0.83 tff(38,plain,(
% 0.85/0.83 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.85/0.83 inference(skolemize,[status(sab)],[37])).
% 0.85/0.83 tff(39,plain,
% 0.85/0.83 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.85/0.83 tff(40,plain,
% 0.85/0.83 (succ(s0, s1) <=> succ(s0, s1)),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.83 tff(41,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 0.85/0.83 tff(42,plain,
% 0.85/0.83 (succ(s0, s1)),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.85/0.83 tff(43,plain,
% 0.85/0.83 (((~![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))),
% 0.85/0.83 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(44,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(45,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.85/0.84 tff(46,plain,
% 0.85/0.84 (trans(s0, s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[45, 42, 39])).
% 0.85/0.84 tff(47,plain,
% 0.85/0.84 (((~![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))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(48,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s0, s1)) | node14(s0, s1))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(49,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s0, s1)) | node14(s0, s1)),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.85/0.84 tff(50,plain,
% 0.85/0.84 (node14(s0, s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[49, 7, 46])).
% 0.85/0.84 tff(51,plain,
% 0.85/0.84 (^[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)))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(52,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[51])).
% 0.85/0.84 tff(53,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(54,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(55,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[54])).
% 0.85/0.84 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')).
% 0.85/0.84 tff(57,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.85/0.84 tff(58,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.85/0.84 tff(59,plain,(
% 0.85/0.84 ![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))),
% 0.85/0.84 inference(skolemize,[status(sab)],[58])).
% 0.85/0.84 tff(60,plain,
% 0.85/0.84 (![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.85/0.84 tff(61,plain,
% 0.85/0.84 (m_main_v_state2(s0, c_n2) <=> m_main_v_state2(s0, c_n2)),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(62,axiom,(m_main_v_state2(s0, c_n2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_12')).
% 0.85/0.84 tff(63,plain,
% 0.85/0.84 (m_main_v_state2(s0, c_n2)),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.85/0.84 tff(64,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(65,plain,
% 0.85/0.84 (((~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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(66,plain,
% 0.85/0.84 (((~![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))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[65])).
% 0.85/0.84 tff(67,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(transitivity,[status(thm)],[66, 64])).
% 0.85/0.84 tff(68,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(69,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.85/0.84 tff(70,plain,
% 0.85/0.84 (m_main_v_state2(s1, c_t2)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[69, 10, 63, 60, 50, 32])).
% 0.85/0.84 tff(71,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(72,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[71])).
% 0.85/0.84 tff(73,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 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')).
% 0.85/0.84 tff(75,plain,
% 0.85/0.84 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.85/0.84 tff(76,plain,(
% 0.85/0.84 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[75])).
% 0.85/0.84 tff(77,plain,
% 0.85/0.84 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.85/0.84 tff(78,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(79,plain,
% 0.85/0.84 ((~![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)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(80,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.85/0.84 tff(81,plain,
% 0.85/0.84 (~m_main_v_state2(s1, c_n2)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[80, 77, 70])).
% 0.85/0.84 tff(82,plain,
% 0.85/0.84 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node9(X))) <=> (m_main_v_state2(X, c_n2) | (~node9(X))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(83,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[82])).
% 0.85/0.84 tff(84,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(85,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_37')).
% 0.85/0.84 tff(86,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.85/0.84 tff(87,plain,(
% 0.85/0.84 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[86])).
% 0.85/0.84 tff(88,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.85/0.84 tff(89,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(90,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s1, c_n2) | (~node9(s1)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(91,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s1, c_n2) | (~node9(s1))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.85/0.84 tff(92,plain,
% 0.85/0.84 (~node9(s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[91, 88, 81])).
% 0.85/0.84 tff(93,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(94,plain,
% 0.85/0.84 ((~![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)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(95,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.85/0.84 tff(96,plain,
% 0.85/0.84 (~m_main_v_state2(s0, c_t2)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[95, 77, 63])).
% 0.85/0.84 tff(97,plain,
% 0.85/0.84 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node15(X))) <=> (m_main_v_state2(X, c_t2) | (~node15(X))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(98,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[97])).
% 0.85/0.84 tff(99,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(100,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_57')).
% 0.85/0.84 tff(101,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.85/0.84 tff(102,plain,(
% 0.85/0.84 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[101])).
% 0.85/0.84 tff(103,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.85/0.84 tff(104,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(105,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s0, c_t2) | (~node15(s0)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(106,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s0, c_t2) | (~node15(s0))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.85/0.84 tff(107,plain,
% 0.85/0.84 (~node15(s0)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[106, 103, 96])).
% 0.85/0.84 tff(108,plain,
% 0.85/0.84 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node16(X))) <=> (m_main_v_state1(X, c_t1) | (~node16(X))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(109,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[108])).
% 0.85/0.84 tff(110,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(111,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_59')).
% 0.85/0.84 tff(112,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.85/0.84 tff(113,plain,(
% 0.85/0.84 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[112])).
% 0.85/0.84 tff(114,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.85/0.84 tff(115,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(116,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | (m_main_v_state1(s0, c_t1) | (~node16(s0)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(117,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node16(X)))) | m_main_v_state1(s0, c_t1) | (~node16(s0))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.85/0.84 tff(118,plain,
% 0.85/0.84 (~node16(s0)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[117, 114, 21])).
% 0.85/0.84 tff(119,plain,
% 0.85/0.84 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node18(X, Y)) <=> ((~trans(X, Y)) | node18(X, Y)))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(120,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[119])).
% 0.85/0.84 tff(121,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(122,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_65')).
% 0.85/0.84 tff(123,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.85/0.84 tff(124,plain,(
% 0.85/0.84 ![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.85/0.84 inference(skolemize,[status(sab)],[123])).
% 0.85/0.84 tff(125,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.85/0.84 tff(126,plain,
% 0.85/0.84 (((~![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))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(127,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s0, s1)) | node18(s0, s1))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(128,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s0, s1)) | node18(s0, s1)),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.85/0.84 tff(129,plain,
% 0.85/0.84 (node18(s0, s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[128, 125, 46])).
% 0.85/0.84 tff(130,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(131,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[130])).
% 0.85/0.84 tff(132,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(133,plain,
% 0.85/0.84 (^[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)))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(134,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[133])).
% 0.85/0.84 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')).
% 0.85/0.84 tff(136,plain,
% 0.85/0.84 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.85/0.84 tff(137,plain,
% 0.85/0.84 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.85/0.84 tff(138,plain,(
% 0.85/0.84 ![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[137])).
% 0.85/0.84 tff(139,plain,
% 0.85/0.84 (![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.85/0.84 tff(140,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(141,plain,
% 0.85/0.84 ((node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1))) <=> (node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(142,plain,
% 0.85/0.84 (((~![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))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[141])).
% 0.85/0.84 tff(143,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(transitivity,[status(thm)],[142, 140])).
% 0.85/0.84 tff(144,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s0) | node16(s0) | node17(s0, s1) | (~node18(s0, s1)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(145,plain,
% 0.85/0.84 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node16(s0) | node15(s0) | node17(s0, s1) | (~node18(s0, s1))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.85/0.84 tff(146,plain,
% 0.85/0.84 (node17(s0, s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[145, 139, 129, 118, 107])).
% 0.85/0.84 tff(147,plain,
% 0.85/0.84 (m_main_v_turn(s0, c_1) <=> m_main_v_turn(s0, c_1)),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(148,axiom,(m_main_v_turn(s0, c_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_13')).
% 0.85/0.84 tff(149,plain,
% 0.85/0.84 (m_main_v_turn(s0, c_1)),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.85/0.84 tff(150,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(151,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[150])).
% 0.85/0.84 tff(152,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 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')).
% 0.85/0.84 tff(154,plain,
% 0.85/0.84 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.85/0.84 tff(155,plain,(
% 0.85/0.84 ![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[154])).
% 0.85/0.84 tff(156,plain,
% 0.85/0.84 (![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.85/0.84 tff(157,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(158,plain,
% 0.85/0.84 ((~![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)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(159,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.85/0.84 tff(160,plain,
% 0.85/0.84 (~m_main_v_turn(s0, c_2)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 0.85/0.84 tff(161,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(162,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[161])).
% 0.85/0.84 tff(163,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(164,plain,
% 0.85/0.84 (^[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))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(165,plain,
% 0.85/0.84 (![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)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[164])).
% 0.85/0.84 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')).
% 0.85/0.84 tff(167,plain,
% 0.85/0.84 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.85/0.84 tff(168,plain,
% 0.85/0.84 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.85/0.84 tff(169,plain,(
% 0.85/0.84 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[168])).
% 0.85/0.84 tff(170,plain,
% 0.85/0.84 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | m_main_v_turn(X, V) | (~m_main_v_turn(Y, V)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.85/0.84 tff(171,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(172,plain,
% 0.85/0.84 (((~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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(173,plain,
% 0.85/0.84 (((~![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))))),
% 0.85/0.84 inference(monotonicity,[status(thm)],[172])).
% 0.85/0.84 tff(174,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(transitivity,[status(thm)],[173, 171])).
% 0.85/0.84 tff(175,plain,
% 0.85/0.84 ((~![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)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(176,plain,
% 0.85/0.84 ((~![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))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.85/0.84 tff(177,plain,
% 0.85/0.84 (~m_main_v_turn(s1, c_2)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[176, 170, 160, 146])).
% 0.85/0.84 tff(178,plain,
% 0.85/0.84 (^[X: $i] : refl((m_main_v_turn(X, c_2) | (~node12(X))) <=> (m_main_v_turn(X, c_2) | (~node12(X))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(179,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[178])).
% 0.85/0.84 tff(180,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X))) <=> ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(181,axiom,(![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_45')).
% 0.85/0.84 tff(182,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.85/0.84 tff(183,plain,(
% 0.85/0.84 ![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[182])).
% 0.85/0.84 tff(184,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.85/0.84 tff(185,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(186,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s1, c_2) | (~node12(s1)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(187,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s1, c_2) | (~node12(s1))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.85/0.84 tff(188,plain,
% 0.85/0.84 (~node12(s1)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[187, 184, 177])).
% 0.85/0.84 tff(189,plain,
% 0.85/0.84 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node1(X))) <=> (m_main_v_state2(X, c_t2) | (~node1(X))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(190,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[189])).
% 0.85/0.84 tff(191,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(192,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_15')).
% 0.85/0.84 tff(193,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.85/0.84 tff(194,plain,(
% 0.85/0.84 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.85/0.84 inference(skolemize,[status(sab)],[193])).
% 0.85/0.84 tff(195,plain,
% 0.85/0.84 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.85/0.84 tff(196,plain,
% 0.85/0.84 (((~![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)))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(197,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s0, c_t2) | (~node1(s0)))),
% 0.85/0.84 inference(quant_inst,[status(thm)],[])).
% 0.85/0.84 tff(198,plain,
% 0.85/0.84 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s0, c_t2) | (~node1(s0))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.85/0.84 tff(199,plain,
% 0.85/0.84 (~node1(s0)),
% 0.85/0.84 inference(unit_resolution,[status(thm)],[198, 195, 96])).
% 0.85/0.84 tff(200,plain,
% 0.85/0.84 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | node7(X, Y)) <=> ((~trans(X, Y)) | node7(X, Y)))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(201,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[200])).
% 0.85/0.84 tff(202,plain,
% 0.85/0.84 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(203,axiom,(![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_34')).
% 0.85/0.85 tff(204,plain,
% 0.85/0.85 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.85/0.85 tff(205,plain,(
% 0.85/0.85 ![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.85/0.85 inference(skolemize,[status(sab)],[204])).
% 0.85/0.85 tff(206,plain,
% 0.85/0.85 (![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.85/0.85 tff(207,plain,
% 0.85/0.85 (((~![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))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(208,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s0, s1)) | node7(s0, s1))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(209,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s0, s1)) | node7(s0, s1)),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.85/0.85 tff(210,plain,
% 0.85/0.85 (node7(s0, s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[209, 206, 46])).
% 0.85/0.85 tff(211,plain,
% 0.85/0.85 (^[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)))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(212,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[211])).
% 0.85/0.85 tff(213,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(214,plain,
% 0.85/0.85 (^[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))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(215,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[214])).
% 0.85/0.85 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')).
% 0.85/0.85 tff(217,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.85/0.85 tff(218,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.85/0.85 tff(219,plain,(
% 0.85/0.85 ![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))),
% 0.85/0.85 inference(skolemize,[status(sab)],[218])).
% 0.85/0.85 tff(220,plain,
% 0.85/0.85 (![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.85/0.85 tff(221,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(222,plain,
% 0.85/0.85 (((~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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(223,plain,
% 0.85/0.85 (((~![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))))),
% 0.85/0.85 inference(monotonicity,[status(thm)],[222])).
% 0.85/0.85 tff(224,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(transitivity,[status(thm)],[223, 221])).
% 0.85/0.85 tff(225,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(226,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.85/0.85 tff(227,plain,
% 0.85/0.85 (m_main_v_state1(s1, c_t1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[226, 10, 63, 220, 210, 199])).
% 0.85/0.85 tff(228,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(229,plain,
% 0.85/0.85 ((~![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)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(230,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.85/0.85 tff(231,plain,
% 0.85/0.85 (~m_main_v_state1(s1, c_n1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[230, 17, 227])).
% 0.85/0.85 tff(232,plain,
% 0.85/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node11(X))) <=> (m_main_v_state1(X, c_n1) | (~node11(X))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(233,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[232])).
% 0.85/0.85 tff(234,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(235,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_42')).
% 0.85/0.85 tff(236,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.85/0.85 tff(237,plain,(
% 0.85/0.85 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[236])).
% 0.85/0.85 tff(238,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.85/0.85 tff(239,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(240,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s1, c_n1) | (~node11(s1)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(241,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s1, c_n1) | (~node11(s1))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.85/0.85 tff(242,plain,
% 0.85/0.85 (~node11(s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[241, 238, 231])).
% 0.85/0.85 tff(243,plain,
% 0.85/0.85 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node10(X))) <=> (m_main_v_state2(X, c_n2) | (~node10(X))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(244,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[243])).
% 0.85/0.85 tff(245,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(246,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_39')).
% 0.85/0.85 tff(247,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.85/0.85 tff(248,plain,(
% 0.85/0.85 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[247])).
% 0.85/0.85 tff(249,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.85/0.85 tff(250,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(251,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s1, c_n2) | (~node10(s1)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(252,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s1, c_n2) | (~node10(s1))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.85/0.85 tff(253,plain,
% 0.85/0.85 (~node10(s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[252, 249, 81])).
% 0.85/0.85 tff(254,plain,
% 0.85/0.85 (^[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))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(255,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[254])).
% 0.85/0.85 tff(256,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 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')).
% 0.85/0.85 tff(258,plain,
% 0.85/0.85 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.85/0.85 tff(259,plain,(
% 0.85/0.85 ![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[258])).
% 0.85/0.85 tff(260,plain,
% 0.85/0.85 (![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.85/0.85 tff(261,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(262,plain,
% 0.85/0.85 ((~![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)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(263,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.85/0.85 tff(264,plain,
% 0.85/0.85 (~m_main_v_state2(s1, c_c2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[263, 260, 70])).
% 0.85/0.85 tff(265,plain,
% 0.85/0.85 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node8(X))) <=> (m_main_v_state2(X, c_n2) | (~node8(X))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(266,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[265])).
% 0.85/0.85 tff(267,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(268,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_35')).
% 0.85/0.85 tff(269,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.85/0.85 tff(270,plain,(
% 0.85/0.85 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[269])).
% 0.85/0.85 tff(271,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.85/0.85 tff(272,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(273,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s1, c_n2) | (~node8(s1)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(274,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s1, c_n2) | (~node8(s1))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.85/0.85 tff(275,plain,
% 0.85/0.85 (~node8(s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[274, 271, 81])).
% 0.85/0.85 tff(276,plain,
% 0.85/0.85 (succ(s1, s2) <=> succ(s1, s2)),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(277,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 0.85/0.85 tff(278,plain,
% 0.85/0.85 (succ(s1, s2)),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.85/0.85 tff(279,plain,
% 0.85/0.85 (((~![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))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(280,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(281,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.85/0.85 tff(282,plain,
% 0.85/0.85 (trans(s1, s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[281, 278, 39])).
% 0.85/0.85 tff(283,plain,
% 0.85/0.85 (((~![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))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(284,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s1, s2)) | node14(s1, s2))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(285,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s1, s2)) | node14(s1, s2)),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.85/0.85 tff(286,plain,
% 0.85/0.85 (node14(s1, s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[285, 7, 282])).
% 0.85/0.85 tff(287,plain,
% 0.85/0.85 (^[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))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(288,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[287])).
% 0.85/0.85 tff(289,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(290,plain,
% 0.85/0.85 (^[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)))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(291,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[290])).
% 0.85/0.85 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')).
% 0.85/0.85 tff(293,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.85/0.85 tff(294,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.85/0.85 tff(295,plain,(
% 0.85/0.85 ![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)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[294])).
% 0.85/0.85 tff(296,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.85/0.85 tff(297,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(298,plain,
% 0.85/0.85 ((~![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)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(299,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.85/0.85 tff(300,plain,
% 0.85/0.85 (m_main_v_state2(s1, c_c2) | node9(s1) | node8(s1) | node10(s1) | node11(s1) | node12(s1) | node13(s1, s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[299, 296, 286])).
% 0.85/0.85 tff(301,plain,
% 0.85/0.85 (node13(s1, s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[300, 275, 264, 253, 242, 188, 92])).
% 0.85/0.85 tff(302,plain,
% 0.85/0.85 (^[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))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(303,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[302])).
% 0.85/0.85 tff(304,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(305,plain,
% 0.85/0.85 (^[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))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(306,plain,
% 0.85/0.85 (![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)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[305])).
% 0.85/0.85 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')).
% 0.85/0.85 tff(308,plain,
% 0.85/0.85 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.85/0.85 tff(309,plain,
% 0.85/0.85 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.85/0.85 tff(310,plain,(
% 0.85/0.85 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[309])).
% 0.85/0.85 tff(311,plain,
% 0.85/0.85 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.85/0.85 tff(312,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(313,plain,
% 0.85/0.85 (((~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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(314,plain,
% 0.85/0.85 (((~![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))))),
% 0.85/0.85 inference(monotonicity,[status(thm)],[313])).
% 0.85/0.85 tff(315,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(transitivity,[status(thm)],[314, 312])).
% 0.85/0.85 tff(316,plain,
% 0.85/0.85 ((~![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)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(317,plain,
% 0.85/0.85 ((~![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))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.85/0.85 tff(318,plain,
% 0.85/0.85 (~m_main_v_state2(s2, c_n2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[317, 311, 81, 301])).
% 0.85/0.85 tff(319,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(320,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s2, c_n2) | (~node9(s2)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(321,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s2, c_n2) | (~node9(s2))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.85/0.85 tff(322,plain,
% 0.85/0.85 (~node9(s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[321, 88, 318])).
% 0.85/0.85 tff(323,plain,
% 0.85/0.85 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node16(X))) <=> (m_main_v_state2(X, c_n2) | (~node16(X))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(324,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[323])).
% 0.85/0.85 tff(325,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(326,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_58')).
% 0.85/0.85 tff(327,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.85/0.85 tff(328,plain,(
% 0.85/0.85 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[327])).
% 0.85/0.85 tff(329,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.85/0.85 tff(330,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(331,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | (m_main_v_state2(s1, c_n2) | (~node16(s1)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(332,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node16(X)))) | m_main_v_state2(s1, c_n2) | (~node16(s1))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.85/0.85 tff(333,plain,
% 0.85/0.85 (~node16(s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[332, 329, 81])).
% 0.85/0.85 tff(334,plain,
% 0.85/0.85 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node15(X))) <=> (m_main_v_state1(X, c_n1) | (~node15(X))))),
% 0.85/0.85 inference(bind,[status(th)],[])).
% 0.85/0.85 tff(335,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.85/0.85 inference(quant_intro,[status(thm)],[334])).
% 0.85/0.85 tff(336,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(337,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_56')).
% 0.85/0.85 tff(338,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.85/0.85 tff(339,plain,(
% 0.85/0.85 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.85/0.85 inference(skolemize,[status(sab)],[338])).
% 0.85/0.85 tff(340,plain,
% 0.85/0.85 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[339, 335])).
% 0.85/0.85 tff(341,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(342,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | (m_main_v_state1(s1, c_n1) | (~node15(s1)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(343,plain,
% 0.85/0.85 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node15(X)))) | m_main_v_state1(s1, c_n1) | (~node15(s1))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.85/0.85 tff(344,plain,
% 0.85/0.85 (~node15(s1)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[343, 340, 231])).
% 0.85/0.85 tff(345,plain,
% 0.85/0.85 (((~![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))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(346,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s1, s2)) | node18(s1, s2))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(347,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s1, s2)) | node18(s1, s2)),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.85/0.85 tff(348,plain,
% 0.85/0.85 (node18(s1, s2)),
% 0.85/0.85 inference(unit_resolution,[status(thm)],[347, 125, 282])).
% 0.85/0.85 tff(349,plain,
% 0.85/0.85 (((~![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)))),
% 0.85/0.85 inference(rewrite,[status(thm)],[])).
% 0.85/0.85 tff(350,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | (node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2)))),
% 0.85/0.85 inference(quant_inst,[status(thm)],[])).
% 0.85/0.85 tff(351,plain,
% 0.85/0.85 ((~![Y: $i, X: $i] : (node15(X) | node16(X) | node17(X, Y) | (~node18(X, Y)))) | node15(s1) | node16(s1) | node17(s1, s2) | (~node18(s1, s2))),
% 0.85/0.85 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.85/0.85 tff(352,plain,
% 0.85/0.85 (node15(s1) | node16(s1) | node17(s1, s2)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[351, 139, 348])).
% 0.85/0.86 tff(353,plain,
% 0.85/0.86 (node17(s1, s2)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[352, 344, 333])).
% 0.85/0.86 tff(354,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(355,plain,
% 0.85/0.86 (((~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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(356,plain,
% 0.85/0.86 (((~![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))))),
% 0.85/0.86 inference(monotonicity,[status(thm)],[355])).
% 0.85/0.86 tff(357,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(transitivity,[status(thm)],[356, 354])).
% 0.85/0.86 tff(358,plain,
% 0.85/0.86 ((~![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)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(359,plain,
% 0.85/0.86 ((~![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))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.85/0.86 tff(360,plain,
% 0.85/0.86 (~m_main_v_turn(s2, c_2)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[359, 170, 353, 177])).
% 0.85/0.86 tff(361,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(362,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s2, c_2) | (~node12(s2)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(363,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s2, c_2) | (~node12(s2))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.85/0.86 tff(364,plain,
% 0.85/0.86 (~node12(s2)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[363, 184, 360])).
% 0.85/0.86 tff(365,plain,
% 0.85/0.86 (^[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)))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(366,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[365])).
% 0.85/0.86 tff(367,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(368,plain,
% 0.85/0.86 (^[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))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(369,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[368])).
% 0.85/0.86 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')).
% 0.85/0.86 tff(371,plain,
% 0.85/0.86 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.85/0.86 tff(372,plain,
% 0.85/0.86 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.85/0.86 tff(373,plain,(
% 0.85/0.86 ![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.85/0.86 inference(skolemize,[status(sab)],[372])).
% 0.85/0.86 tff(374,plain,
% 0.85/0.86 (![V: $i, Y: $i, X: $i] : ((~node17(X, Y)) | (~m_main_v_turn(X, V)) | m_main_v_turn(Y, V))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.85/0.86 tff(375,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(376,plain,
% 0.85/0.86 (((~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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(377,plain,
% 0.85/0.86 (((~![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))))),
% 0.85/0.86 inference(monotonicity,[status(thm)],[376])).
% 0.85/0.86 tff(378,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(transitivity,[status(thm)],[377, 375])).
% 0.85/0.86 tff(379,plain,
% 0.85/0.86 ((~![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))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(380,plain,
% 0.85/0.86 ((~![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))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.85/0.86 tff(381,plain,
% 0.85/0.86 (m_main_v_turn(s1, c_1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[380, 149, 374, 146])).
% 0.85/0.86 tff(382,plain,
% 0.85/0.86 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node4(X))) <=> (m_main_v_state2(X, c_n2) | (~node4(X))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(383,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[382])).
% 0.85/0.86 tff(384,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(385,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_21')).
% 0.85/0.86 tff(386,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.85/0.86 tff(387,plain,(
% 0.85/0.86 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.85/0.86 inference(skolemize,[status(sab)],[386])).
% 0.85/0.86 tff(388,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.85/0.86 tff(389,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(390,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s1, c_n2) | (~node4(s1)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(391,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s1, c_n2) | (~node4(s1))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.85/0.86 tff(392,plain,
% 0.85/0.86 (~node4(s1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[391, 388, 81])).
% 0.85/0.86 tff(393,plain,
% 0.85/0.86 (^[X: $i] : refl((m_main_v_state2(X, c_c2) | (~node3(X))) <=> (m_main_v_state2(X, c_c2) | (~node3(X))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(394,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[393])).
% 0.85/0.86 tff(395,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X))) <=> ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(396,axiom,(![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_19')).
% 0.85/0.86 tff(397,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.85/0.86 tff(398,plain,(
% 0.85/0.86 ![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.85/0.86 inference(skolemize,[status(sab)],[397])).
% 0.85/0.86 tff(399,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[398, 394])).
% 0.85/0.86 tff(400,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(401,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s1, c_c2) | (~node3(s1)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(402,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s1, c_c2) | (~node3(s1))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.85/0.86 tff(403,plain,
% 0.85/0.86 (~node3(s1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[402, 399, 264])).
% 0.85/0.86 tff(404,plain,
% 0.85/0.86 (^[X: $i] : refl((m_main_v_state2(X, c_n2) | (~node2(X))) <=> (m_main_v_state2(X, c_n2) | (~node2(X))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(405,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[404])).
% 0.85/0.86 tff(406,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X))) <=> ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(407,axiom,(![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_17')).
% 0.85/0.86 tff(408,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.85/0.86 tff(409,plain,(
% 0.85/0.86 ![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.85/0.86 inference(skolemize,[status(sab)],[408])).
% 0.85/0.86 tff(410,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.85/0.86 tff(411,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(412,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s1, c_n2) | (~node2(s1)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(413,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s1, c_n2) | (~node2(s1))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.85/0.86 tff(414,plain,
% 0.85/0.86 (~node2(s1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[413, 410, 81])).
% 0.85/0.86 tff(415,plain,
% 0.85/0.86 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node1(X))) <=> (m_main_v_state1(X, c_n1) | (~node1(X))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(416,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[415])).
% 0.85/0.86 tff(417,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(418,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_14')).
% 0.85/0.86 tff(419,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.85/0.86 tff(420,plain,(
% 0.85/0.86 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.85/0.86 inference(skolemize,[status(sab)],[419])).
% 0.85/0.86 tff(421,plain,
% 0.85/0.86 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.85/0.86 tff(422,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(423,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s1, c_n1) | (~node1(s1)))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(424,plain,
% 0.85/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s1, c_n1) | (~node1(s1))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.85/0.86 tff(425,plain,
% 0.85/0.86 (~node1(s1)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[424, 421, 231])).
% 0.85/0.86 tff(426,plain,
% 0.85/0.86 (((~![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))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(427,plain,
% 0.85/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s1, s2)) | node7(s1, s2))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(428,plain,
% 0.85/0.86 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s1, s2)) | node7(s1, s2)),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.85/0.86 tff(429,plain,
% 0.85/0.86 (node7(s1, s2)),
% 0.85/0.86 inference(unit_resolution,[status(thm)],[428, 206, 282])).
% 0.85/0.86 tff(430,plain,
% 0.85/0.86 (^[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)))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(431,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[430])).
% 0.85/0.86 tff(432,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(433,plain,
% 0.85/0.86 (^[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))))),
% 0.85/0.86 inference(bind,[status(th)],[])).
% 0.85/0.86 tff(434,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(quant_intro,[status(thm)],[433])).
% 0.85/0.86 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')).
% 0.85/0.86 tff(436,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.85/0.86 tff(437,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.85/0.86 tff(438,plain,(
% 0.85/0.86 ![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))),
% 0.85/0.86 inference(skolemize,[status(sab)],[437])).
% 0.85/0.86 tff(439,plain,
% 0.85/0.86 (![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))),
% 0.85/0.86 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.85/0.86 tff(440,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(441,plain,
% 0.85/0.86 (((~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)))),
% 0.85/0.86 inference(rewrite,[status(thm)],[])).
% 0.85/0.86 tff(442,plain,
% 0.85/0.86 (((~![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))))),
% 0.85/0.86 inference(monotonicity,[status(thm)],[441])).
% 0.85/0.86 tff(443,plain,
% 0.85/0.86 (((~![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)))),
% 0.85/0.86 inference(transitivity,[status(thm)],[442, 440])).
% 0.85/0.86 tff(444,plain,
% 0.85/0.86 ((~![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))),
% 0.85/0.86 inference(quant_inst,[status(thm)],[])).
% 0.85/0.86 tff(445,plain,
% 0.85/0.86 ((~![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))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.95/0.86 tff(446,plain,
% 0.95/0.86 (m_main_v_state1(s2, c_c1) | node1(s1) | node2(s1) | node3(s1) | node4(s1) | (~m_main_v_turn(s1, c_1))),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[445, 439, 429, 70, 227])).
% 0.95/0.86 tff(447,plain,
% 0.95/0.86 (m_main_v_state1(s2, c_c1)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[446, 425, 414, 403, 392, 381])).
% 0.95/0.86 tff(448,plain,
% 0.95/0.86 (^[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))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(449,plain,
% 0.95/0.86 (![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)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[448])).
% 0.95/0.86 tff(450,plain,
% 0.95/0.86 (![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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 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')).
% 0.95/0.86 tff(452,plain,
% 0.95/0.86 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.95/0.86 tff(453,plain,(
% 0.95/0.86 ![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.86 inference(skolemize,[status(sab)],[452])).
% 0.95/0.86 tff(454,plain,
% 0.95/0.86 (![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.95/0.86 tff(455,plain,
% 0.95/0.86 (((~![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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(456,plain,
% 0.95/0.86 ((~![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)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(457,plain,
% 0.95/0.86 ((~![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))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.95/0.86 tff(458,plain,
% 0.95/0.86 (~m_main_v_state1(s2, c_n1)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[457, 454, 447])).
% 0.95/0.86 tff(459,plain,
% 0.95/0.86 (((~![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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(460,plain,
% 0.95/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s2, c_n1) | (~node11(s2)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(461,plain,
% 0.95/0.86 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s2, c_n1) | (~node11(s2))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.95/0.86 tff(462,plain,
% 0.95/0.86 (~node11(s2)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[461, 238, 458])).
% 0.95/0.86 tff(463,plain,
% 0.95/0.86 (((~![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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(464,plain,
% 0.95/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s2, c_n2) | (~node10(s2)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(465,plain,
% 0.95/0.86 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s2, c_n2) | (~node10(s2))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.95/0.86 tff(466,plain,
% 0.95/0.86 (~node10(s2)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[465, 249, 318])).
% 0.95/0.86 tff(467,plain,
% 0.95/0.86 (((~![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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(468,plain,
% 0.95/0.86 (((~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)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(469,plain,
% 0.95/0.86 (((~![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))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[468])).
% 0.95/0.87 tff(470,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[469, 467])).
% 0.95/0.87 tff(471,plain,
% 0.95/0.87 ((~![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)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(472,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.95/0.87 tff(473,plain,
% 0.95/0.87 (~m_main_v_state2(s2, c_c2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[472, 311, 264, 301])).
% 0.95/0.87 tff(474,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(475,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s2, c_n2) | (~node8(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(476,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s2, c_n2) | (~node8(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.95/0.87 tff(477,plain,
% 0.95/0.87 (~node8(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[476, 271, 318])).
% 0.95/0.87 tff(478,plain,
% 0.95/0.87 (succ(s2, s3) <=> succ(s2, s3)),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(479,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 0.95/0.87 tff(480,plain,
% 0.95/0.87 (succ(s2, s3)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.95/0.87 tff(481,plain,
% 0.95/0.87 (((~![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))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(482,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(483,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.95/0.87 tff(484,plain,
% 0.95/0.87 (trans(s2, s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[483, 480, 39])).
% 0.95/0.87 tff(485,plain,
% 0.95/0.87 (((~![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))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(486,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s2, s3)) | node14(s2, s3))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(487,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s2, s3)) | node14(s2, s3)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.95/0.87 tff(488,plain,
% 0.95/0.87 (node14(s2, s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[487, 7, 484])).
% 0.95/0.87 tff(489,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(490,plain,
% 0.95/0.87 ((~![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)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(491,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.95/0.87 tff(492,plain,
% 0.95/0.87 (m_main_v_state2(s2, c_c2) | node9(s2) | node8(s2) | node10(s2) | node11(s2) | node12(s2) | node13(s2, s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[491, 296, 488])).
% 0.95/0.87 tff(493,plain,
% 0.95/0.87 (node13(s2, s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[492, 477, 473, 466, 462, 364, 322])).
% 0.95/0.87 tff(494,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(495,plain,
% 0.95/0.87 (((~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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(496,plain,
% 0.95/0.87 (((~![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))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[495])).
% 0.95/0.87 tff(497,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[496, 494])).
% 0.95/0.87 tff(498,plain,
% 0.95/0.87 ((~![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)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(499,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.95/0.87 tff(500,plain,
% 0.95/0.87 (~m_main_v_state2(s3, c_n2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[499, 311, 318, 493])).
% 0.95/0.87 tff(501,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(502,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s3, c_n2) | (~node9(s3)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(503,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s3, c_n2) | (~node9(s3))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.95/0.87 tff(504,plain,
% 0.95/0.87 (~node9(s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[503, 88, 500])).
% 0.95/0.87 tff(505,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(506,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s3, c_n2) | (~node10(s3)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(507,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s3, c_n2) | (~node10(s3))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.95/0.87 tff(508,plain,
% 0.95/0.87 (~node10(s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[507, 249, 500])).
% 0.95/0.87 tff(509,plain,
% 0.95/0.87 (^[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)))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(510,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[509])).
% 0.95/0.87 tff(511,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(512,plain,
% 0.95/0.87 (^[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))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(513,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[512])).
% 0.95/0.87 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')).
% 0.95/0.87 tff(515,plain,
% 0.95/0.87 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.95/0.87 tff(516,plain,
% 0.95/0.87 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[515, 511])).
% 0.95/0.87 tff(517,plain,(
% 0.95/0.87 ![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.95/0.87 inference(skolemize,[status(sab)],[516])).
% 0.95/0.87 tff(518,plain,
% 0.95/0.87 (![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[517, 510])).
% 0.95/0.87 tff(519,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(520,plain,
% 0.95/0.87 (((~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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(521,plain,
% 0.95/0.87 (((~![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))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[520])).
% 0.95/0.87 tff(522,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[521, 519])).
% 0.95/0.87 tff(523,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(524,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.95/0.87 tff(525,plain,
% 0.95/0.87 (m_main_v_state2(s2, c_t2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[524, 518, 70, 301])).
% 0.95/0.87 tff(526,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(527,plain,
% 0.95/0.87 (((~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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(528,plain,
% 0.95/0.87 (((~![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))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[527])).
% 0.95/0.87 tff(529,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[528, 526])).
% 0.95/0.87 tff(530,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(531,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.95/0.87 tff(532,plain,
% 0.95/0.87 (m_main_v_state2(s3, c_t2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[531, 518, 525, 493])).
% 0.95/0.87 tff(533,plain,
% 0.95/0.87 (^[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))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(534,plain,
% 0.95/0.87 (![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)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[533])).
% 0.95/0.87 tff(535,plain,
% 0.95/0.87 (![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 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')).
% 0.95/0.87 tff(537,plain,
% 0.95/0.87 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.95/0.87 tff(538,plain,(
% 0.95/0.87 ![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.87 inference(skolemize,[status(sab)],[537])).
% 0.95/0.87 tff(539,plain,
% 0.95/0.87 (![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[538, 534])).
% 0.95/0.87 tff(540,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(541,plain,
% 0.95/0.87 ((~![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)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(542,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.95/0.87 tff(543,plain,
% 0.95/0.87 (~m_main_v_state1(s2, c_t1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[542, 539, 447])).
% 0.95/0.87 tff(544,plain,
% 0.95/0.87 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node5(X))) <=> (m_main_v_state1(X, c_t1) | (~node5(X))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(545,plain,
% 0.95/0.87 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[544])).
% 0.95/0.87 tff(546,plain,
% 0.95/0.87 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(547,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_22')).
% 0.95/0.87 tff(548,plain,
% 0.95/0.87 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.95/0.87 tff(549,plain,(
% 0.95/0.87 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.95/0.87 inference(skolemize,[status(sab)],[548])).
% 0.95/0.87 tff(550,plain,
% 0.95/0.87 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[549, 545])).
% 0.95/0.87 tff(551,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(552,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s2, c_t1) | (~node5(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(553,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s2, c_t1) | (~node5(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.95/0.87 tff(554,plain,
% 0.95/0.87 (~node5(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[553, 550, 543])).
% 0.95/0.87 tff(555,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(556,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s2, c_n2) | (~node4(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(557,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s2, c_n2) | (~node4(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.95/0.87 tff(558,plain,
% 0.95/0.87 (~node4(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[557, 388, 318])).
% 0.95/0.87 tff(559,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(560,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s2, c_c2) | (~node3(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(561,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s2, c_c2) | (~node3(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.95/0.87 tff(562,plain,
% 0.95/0.87 (~node3(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[561, 399, 473])).
% 0.95/0.87 tff(563,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(564,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s2, c_n2) | (~node2(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(565,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s2, c_n2) | (~node2(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.95/0.87 tff(566,plain,
% 0.95/0.87 (~node2(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[565, 410, 318])).
% 0.95/0.87 tff(567,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(568,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s2, c_n1) | (~node1(s2)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(569,plain,
% 0.95/0.87 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s2, c_n1) | (~node1(s2))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.95/0.87 tff(570,plain,
% 0.95/0.87 (~node1(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[569, 421, 458])).
% 0.95/0.87 tff(571,plain,
% 0.95/0.87 (((~![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))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(572,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s2, s3)) | node7(s2, s3))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(573,plain,
% 0.95/0.87 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s2, s3)) | node7(s2, s3)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.95/0.87 tff(574,plain,
% 0.95/0.87 (node7(s2, s3)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[573, 206, 484])).
% 0.95/0.87 tff(575,plain,
% 0.95/0.87 (^[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)))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(576,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[575])).
% 0.95/0.87 tff(577,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(578,plain,
% 0.95/0.87 (^[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))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(579,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[578])).
% 0.95/0.87 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')).
% 0.95/0.87 tff(581,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.95/0.87 tff(582,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[581, 577])).
% 0.95/0.87 tff(583,plain,(
% 0.95/0.87 ![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))),
% 0.95/0.87 inference(skolemize,[status(sab)],[582])).
% 0.95/0.87 tff(584,plain,
% 0.95/0.87 (![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[583, 576])).
% 0.95/0.87 tff(585,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(586,plain,
% 0.95/0.87 (((~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)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(587,plain,
% 0.95/0.87 (((~![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))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[586])).
% 0.95/0.87 tff(588,plain,
% 0.95/0.87 (((~![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)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[587, 585])).
% 0.95/0.87 tff(589,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(590,plain,
% 0.95/0.87 ((~![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))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.95/0.87 tff(591,plain,
% 0.95/0.87 (m_main_v_state1(s3, c_n1) | (~m_main_v_state1(s2, c_c1)) | node1(s2) | node2(s2) | node3(s2) | node4(s2) | node5(s2)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[590, 584, 574])).
% 0.95/0.87 tff(592,plain,
% 0.95/0.87 (m_main_v_state1(s3, c_n1)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[591, 570, 447, 566, 562, 558, 554])).
% 0.95/0.88 tff(593,plain,
% 0.95/0.88 (((~![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)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(594,plain,
% 0.95/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s3, c_n2) | (~node8(s3)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(595,plain,
% 0.95/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s3, c_n2) | (~node8(s3))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.95/0.88 tff(596,plain,
% 0.95/0.88 (~node8(s3)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[595, 271, 500])).
% 0.95/0.88 tff(597,plain,
% 0.95/0.88 (succ(s3, s4) <=> succ(s3, s4)),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(598,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 0.95/0.88 tff(599,plain,
% 0.95/0.88 (succ(s3, s4)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[598, 597])).
% 0.95/0.88 tff(600,plain,
% 0.95/0.88 (((~![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(601,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(602,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.95/0.88 tff(603,plain,
% 0.95/0.88 (trans(s3, s4)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[602, 599, 39])).
% 0.95/0.88 tff(604,plain,
% 0.95/0.88 (((~![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(605,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s3, s4)) | node14(s3, s4))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(606,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s3, s4)) | node14(s3, s4)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.95/0.88 tff(607,plain,
% 0.95/0.88 (node14(s3, s4)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[606, 7, 603])).
% 0.95/0.88 tff(608,plain,
% 0.95/0.88 (^[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)))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(609,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[608])).
% 0.95/0.88 tff(610,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(611,plain,
% 0.95/0.88 (^[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))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(612,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[611])).
% 0.95/0.88 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')).
% 0.95/0.88 tff(614,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.95/0.88 tff(615,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.95/0.88 tff(616,plain,(
% 0.95/0.88 ![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))),
% 0.95/0.88 inference(skolemize,[status(sab)],[615])).
% 0.95/0.88 tff(617,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.95/0.88 tff(618,plain,
% 0.95/0.88 (((~![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(619,plain,
% 0.95/0.88 ((~![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))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(620,plain,
% 0.95/0.88 ((~![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)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.95/0.88 tff(621,plain,
% 0.95/0.88 ((~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)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[620, 617, 607])).
% 0.95/0.88 tff(622,plain,
% 0.95/0.88 (m_main_v_state2(s4, c_c2)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[621, 596, 592, 532, 508, 504])).
% 0.95/0.88 tff(623,plain,
% 0.95/0.88 (((~![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)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(624,plain,
% 0.95/0.88 ((~![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)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(625,plain,
% 0.95/0.88 ((~![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.95/0.88 tff(626,plain,
% 0.95/0.88 (~m_main_v_state2(s4, c_t2)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[625, 260, 622])).
% 0.95/0.88 tff(627,plain,
% 0.95/0.88 (^[X: $i] : refl((m_main_v_state2(X, c_t2) | (~node12(X))) <=> (m_main_v_state2(X, c_t2) | (~node12(X))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(628,plain,
% 0.95/0.88 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[627])).
% 0.95/0.88 tff(629,plain,
% 0.95/0.88 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X))) <=> ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(630,axiom,(![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_43')).
% 0.95/0.88 tff(631,plain,
% 0.95/0.88 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.95/0.88 tff(632,plain,(
% 0.95/0.88 ![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.95/0.88 inference(skolemize,[status(sab)],[631])).
% 0.95/0.88 tff(633,plain,
% 0.95/0.88 (![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[632, 628])).
% 0.95/0.88 tff(634,plain,
% 0.95/0.88 (((~![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)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(635,plain,
% 0.95/0.88 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s4, c_t2) | (~node12(s4)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(636,plain,
% 0.95/0.88 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s4, c_t2) | (~node12(s4))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.95/0.88 tff(637,plain,
% 0.95/0.88 (~node12(s4)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[636, 633, 626])).
% 0.95/0.88 tff(638,plain,
% 0.95/0.88 (((~![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(639,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s3, s4)) | node7(s3, s4))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(640,plain,
% 0.95/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s3, s4)) | node7(s3, s4)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.95/0.88 tff(641,plain,
% 0.95/0.88 (node7(s3, s4)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[640, 206, 603])).
% 0.95/0.88 tff(642,plain,
% 0.95/0.88 (^[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)))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(643,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[642])).
% 0.95/0.88 tff(644,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(645,plain,
% 0.95/0.88 (^[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))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(646,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[645])).
% 0.95/0.88 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')).
% 0.95/0.88 tff(648,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.95/0.88 tff(649,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[648, 644])).
% 0.95/0.88 tff(650,plain,(
% 0.95/0.88 ![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))),
% 0.95/0.88 inference(skolemize,[status(sab)],[649])).
% 0.95/0.88 tff(651,plain,
% 0.95/0.88 (![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))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[650, 643])).
% 0.95/0.88 tff(652,plain,
% 0.95/0.88 (((~![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))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(653,plain,
% 0.96/0.88 ((~![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))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(654,plain,
% 0.96/0.88 ((~![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)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.96/0.88 tff(655,plain,
% 0.96/0.88 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_state1(s4, c_t1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[654, 651, 641])).
% 0.96/0.88 tff(656,plain,
% 0.96/0.88 (m_main_v_state1(s4, c_t1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[655, 532, 592])).
% 0.96/0.88 tff(657,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(658,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(659,plain,
% 0.96/0.88 ((~![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))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.96/0.88 tff(660,plain,
% 0.96/0.88 (~m_main_v_state1(s4, c_n1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[659, 17, 656])).
% 0.96/0.88 tff(661,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(662,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s4, c_n1) | (~node11(s4)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(663,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s4, c_n1) | (~node11(s4))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.96/0.88 tff(664,plain,
% 0.96/0.88 (~node11(s4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[663, 238, 660])).
% 0.96/0.88 tff(665,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(666,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(667,plain,
% 0.96/0.88 ((~![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))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.96/0.88 tff(668,plain,
% 0.96/0.88 (~m_main_v_state1(s4, c_c1)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[667, 539, 656])).
% 0.96/0.88 tff(669,plain,
% 0.96/0.88 (^[X: $i] : refl((m_main_v_state1(X, c_c1) | (~node10(X))) <=> (m_main_v_state1(X, c_c1) | (~node10(X))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(670,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[669])).
% 0.96/0.88 tff(671,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X))) <=> ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(672,axiom,(![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_40')).
% 0.96/0.88 tff(673,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.96/0.88 tff(674,plain,(
% 0.96/0.88 ![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[673])).
% 0.96/0.88 tff(675,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[674, 670])).
% 0.96/0.88 tff(676,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(677,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s4, c_c1) | (~node10(s4)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(678,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s4, c_c1) | (~node10(s4))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.96/0.88 tff(679,plain,
% 0.96/0.88 (~node10(s4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[678, 675, 668])).
% 0.96/0.88 tff(680,plain,
% 0.96/0.88 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node9(X))) <=> (m_main_v_state1(X, c_n1) | (~node9(X))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(681,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[680])).
% 0.96/0.88 tff(682,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(683,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_38')).
% 0.96/0.88 tff(684,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.96/0.88 tff(685,plain,(
% 0.96/0.88 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[684])).
% 0.96/0.88 tff(686,plain,
% 0.96/0.88 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[685, 681])).
% 0.96/0.88 tff(687,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(688,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s4, c_n1) | (~node9(s4)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(689,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s4, c_n1) | (~node9(s4))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.96/0.88 tff(690,plain,
% 0.96/0.88 (~node9(s4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[689, 686, 660])).
% 0.96/0.88 tff(691,plain,
% 0.96/0.88 (^[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))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(692,plain,
% 0.96/0.88 (![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)))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[691])).
% 0.96/0.88 tff(693,plain,
% 0.96/0.88 (![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 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')).
% 0.96/0.88 tff(695,plain,
% 0.96/0.88 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.96/0.88 tff(696,plain,(
% 0.96/0.88 ![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.96/0.88 inference(skolemize,[status(sab)],[695])).
% 0.96/0.88 tff(697,plain,
% 0.96/0.88 (![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[696, 692])).
% 0.96/0.88 tff(698,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(699,plain,
% 0.96/0.88 ((~![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)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(700,plain,
% 0.96/0.88 ((~![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))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.96/0.88 tff(701,plain,
% 0.96/0.88 (~m_main_v_state2(s4, c_n2)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[700, 697, 622])).
% 0.96/0.88 tff(702,plain,
% 0.96/0.88 (((~![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)))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(703,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s4, c_n2) | (~node8(s4)))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(704,plain,
% 0.96/0.88 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s4, c_n2) | (~node8(s4))),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.96/0.88 tff(705,plain,
% 0.96/0.88 (~node8(s4)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[704, 271, 701])).
% 0.96/0.88 tff(706,plain,
% 0.96/0.88 (succ(s4, s5) <=> succ(s4, s5)),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(707,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 0.96/0.88 tff(708,plain,
% 0.96/0.88 (succ(s4, s5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.96/0.88 tff(709,plain,
% 0.96/0.88 (((~![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))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(710,plain,
% 0.96/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(711,plain,
% 0.96/0.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.96/0.88 tff(712,plain,
% 0.96/0.88 (trans(s4, s5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[711, 708, 39])).
% 0.96/0.88 tff(713,plain,
% 0.96/0.88 (((~![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))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(714,plain,
% 0.96/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s4, s5)) | node14(s4, s5))),
% 0.96/0.88 inference(quant_inst,[status(thm)],[])).
% 0.96/0.88 tff(715,plain,
% 0.96/0.88 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s4, s5)) | node14(s4, s5)),
% 0.96/0.88 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.96/0.88 tff(716,plain,
% 0.96/0.88 (node14(s4, s5)),
% 0.96/0.88 inference(unit_resolution,[status(thm)],[715, 7, 712])).
% 0.96/0.88 tff(717,plain,
% 0.96/0.88 (^[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)))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(718,plain,
% 0.96/0.88 (![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))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[717])).
% 0.96/0.88 tff(719,plain,
% 0.96/0.88 (![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))),
% 0.96/0.88 inference(rewrite,[status(thm)],[])).
% 0.96/0.88 tff(720,plain,
% 0.96/0.88 (^[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))))),
% 0.96/0.88 inference(bind,[status(th)],[])).
% 0.96/0.88 tff(721,plain,
% 0.96/0.88 (![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))),
% 0.96/0.88 inference(quant_intro,[status(thm)],[720])).
% 0.96/0.89 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')).
% 0.96/0.89 tff(723,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.96/0.89 tff(724,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[723, 719])).
% 0.96/0.89 tff(725,plain,(
% 0.96/0.89 ![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))),
% 0.96/0.89 inference(skolemize,[status(sab)],[724])).
% 0.96/0.89 tff(726,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[725, 718])).
% 0.96/0.89 tff(727,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(728,plain,
% 0.96/0.89 (((~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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(729,plain,
% 0.96/0.89 (((~![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))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[728])).
% 0.96/0.89 tff(730,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[729, 727])).
% 0.96/0.89 tff(731,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(732,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.96/0.89 tff(733,plain,
% 0.96/0.89 (m_main_v_state2(s5, c_n2) | node9(s4) | node8(s4) | node10(s4) | node11(s4) | node12(s4) | (~m_main_v_state2(s4, c_c2))),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[732, 726, 716])).
% 0.96/0.89 tff(734,plain,
% 0.96/0.89 (m_main_v_state2(s5, c_n2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[733, 705, 622, 690, 679, 664, 637])).
% 0.96/0.89 tff(735,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(736,plain,
% 0.96/0.89 ((~![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)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(737,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.96/0.89 tff(738,plain,
% 0.96/0.89 (~m_main_v_state2(s5, c_c2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[737, 697, 734])).
% 0.96/0.89 tff(739,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(740,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s5, c_c2) | (~node3(s5)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(741,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s5, c_c2) | (~node3(s5))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.96/0.89 tff(742,plain,
% 0.96/0.89 (~node3(s5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[741, 399, 738])).
% 0.96/0.89 tff(743,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(744,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s4, c_n1) | (~node1(s4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(745,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s4, c_n1) | (~node1(s4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.96/0.89 tff(746,plain,
% 0.96/0.89 (~node1(s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[745, 421, 660])).
% 0.96/0.89 tff(747,plain,
% 0.96/0.89 (((~![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))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(748,plain,
% 0.96/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s3, s4)) | node18(s3, s4))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(749,plain,
% 0.96/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s3, s4)) | node18(s3, s4)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.96/0.89 tff(750,plain,
% 0.96/0.89 (node18(s3, s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[749, 125, 603])).
% 0.96/0.89 tff(751,plain,
% 0.96/0.89 (^[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)))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(752,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[751])).
% 0.96/0.89 tff(753,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(754,plain,
% 0.96/0.89 (^[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))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(755,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[754])).
% 0.96/0.89 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')).
% 0.96/0.89 tff(757,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.96/0.89 tff(758,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[757, 753])).
% 0.96/0.89 tff(759,plain,(
% 0.96/0.89 ![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))),
% 0.96/0.89 inference(skolemize,[status(sab)],[758])).
% 0.96/0.89 tff(760,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[759, 752])).
% 0.96/0.89 tff(761,plain,
% 0.96/0.89 (((~![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))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(762,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(763,plain,
% 0.96/0.89 ((~![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)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.96/0.89 tff(764,plain,
% 0.96/0.89 ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state2(s3, c_t2)) | m_main_v_turn(s4, c_2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[763, 760, 750])).
% 0.96/0.89 tff(765,plain,
% 0.96/0.89 (m_main_v_turn(s4, c_2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[764, 532, 592])).
% 0.96/0.89 tff(766,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(767,plain,
% 0.96/0.89 ((~![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)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(768,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.96/0.89 tff(769,plain,
% 0.96/0.89 (~m_main_v_turn(s4, c_1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[768, 156, 765])).
% 0.96/0.89 tff(770,plain,
% 0.96/0.89 (^[X: $i] : refl((m_main_v_turn(X, c_1) | (~node5(X))) <=> (m_main_v_turn(X, c_1) | (~node5(X))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(771,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[770])).
% 0.96/0.89 tff(772,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X))) <=> ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(773,axiom,(![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_24')).
% 0.96/0.89 tff(774,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.96/0.89 tff(775,plain,(
% 0.96/0.89 ![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[774])).
% 0.96/0.89 tff(776,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[775, 771])).
% 0.96/0.89 tff(777,plain,
% 0.96/0.89 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s4, c_1) | (~node5(s4)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s4, c_1) | (~node5(s4)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(778,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s4, c_1) | (~node5(s4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(779,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s4, c_1) | (~node5(s4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.96/0.89 tff(780,plain,
% 0.96/0.89 (~node5(s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[779, 776, 769])).
% 0.96/0.89 tff(781,plain,
% 0.96/0.89 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node2(X))) <=> (m_main_v_state1(X, c_n1) | (~node2(X))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(782,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[781])).
% 0.96/0.89 tff(783,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(784,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_16')).
% 0.96/0.89 tff(785,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.96/0.89 tff(786,plain,(
% 0.96/0.89 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[785])).
% 0.96/0.89 tff(787,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[786, 782])).
% 0.96/0.89 tff(788,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(789,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s4, c_n1) | (~node2(s4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(790,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s4, c_n1) | (~node2(s4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.96/0.89 tff(791,plain,
% 0.96/0.89 (~node2(s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[790, 787, 660])).
% 0.96/0.89 tff(792,plain,
% 0.96/0.89 (^[X: $i] : refl((m_main_v_state1(X, c_n1) | (~node3(X))) <=> (m_main_v_state1(X, c_n1) | (~node3(X))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(793,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[792])).
% 0.96/0.89 tff(794,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X))) <=> ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(795,axiom,(![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_18')).
% 0.96/0.89 tff(796,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.96/0.89 tff(797,plain,(
% 0.96/0.89 ![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[796])).
% 0.96/0.89 tff(798,plain,
% 0.96/0.89 (![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[797, 793])).
% 0.96/0.89 tff(799,plain,
% 0.96/0.89 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s4, c_n1) | (~node3(s4)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s4, c_n1) | (~node3(s4)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(800,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s4, c_n1) | (~node3(s4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(801,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s4, c_n1) | (~node3(s4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[800, 799])).
% 0.96/0.89 tff(802,plain,
% 0.96/0.89 (~node3(s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[801, 798, 660])).
% 0.96/0.89 tff(803,plain,
% 0.96/0.89 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s4, c_n2) | (~node4(s4)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s4, c_n2) | (~node4(s4)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(804,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s4, c_n2) | (~node4(s4)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(805,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s4, c_n2) | (~node4(s4))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.96/0.89 tff(806,plain,
% 0.96/0.89 (~node4(s4)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[805, 388, 701])).
% 0.96/0.89 tff(807,plain,
% 0.96/0.89 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s4, s5)) | node7(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s4, s5)) | node7(s4, s5))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(808,plain,
% 0.96/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s4, s5)) | node7(s4, s5))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(809,plain,
% 0.96/0.89 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s4, s5)) | node7(s4, s5)),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.96/0.89 tff(810,plain,
% 0.96/0.89 (node7(s4, s5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[809, 206, 712])).
% 0.96/0.89 tff(811,plain,
% 0.96/0.89 (^[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))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(812,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[811])).
% 0.96/0.89 tff(813,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(814,plain,
% 0.96/0.89 (^[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)))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(815,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[814])).
% 0.96/0.89 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')).
% 0.96/0.89 tff(817,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.96/0.89 tff(818,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[817, 813])).
% 0.96/0.89 tff(819,plain,(
% 0.96/0.89 ![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)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[818])).
% 0.96/0.89 tff(820,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[819, 812])).
% 0.96/0.89 tff(821,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(822,plain,
% 0.96/0.89 ((~![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)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(823,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.96/0.89 tff(824,plain,
% 0.96/0.89 (m_main_v_state1(s4, c_c1) | node1(s4) | node2(s4) | node3(s4) | node4(s4) | node5(s4) | node6(s4, s5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[823, 820, 810])).
% 0.96/0.89 tff(825,plain,
% 0.96/0.89 (node6(s4, s5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[824, 806, 668, 802, 791, 780, 746])).
% 0.96/0.89 tff(826,plain,
% 0.96/0.89 (^[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))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(827,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[826])).
% 0.96/0.89 tff(828,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(829,plain,
% 0.96/0.89 (^[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))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(830,plain,
% 0.96/0.89 (![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)))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[829])).
% 0.96/0.89 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')).
% 0.96/0.89 tff(832,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[831, 830])).
% 0.96/0.89 tff(833,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[832, 828])).
% 0.96/0.89 tff(834,plain,(
% 0.96/0.89 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.96/0.89 inference(skolemize,[status(sab)],[833])).
% 0.96/0.89 tff(835,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[834, 827])).
% 0.96/0.89 tff(836,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(837,plain,
% 0.96/0.89 (((~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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(838,plain,
% 0.96/0.89 (((~![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))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[837])).
% 0.96/0.89 tff(839,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[838, 836])).
% 0.96/0.89 tff(840,plain,
% 0.96/0.89 ((~![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)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(841,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.96/0.89 tff(842,plain,
% 0.96/0.89 (~m_main_v_state1(s5, c_n1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[841, 835, 660, 825])).
% 0.96/0.89 tff(843,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(844,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s5, c_n1) | (~node2(s5)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(845,plain,
% 0.96/0.89 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s5, c_n1) | (~node2(s5))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.96/0.89 tff(846,plain,
% 0.96/0.89 (~node2(s5)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[845, 787, 842])).
% 0.96/0.89 tff(847,plain,
% 0.96/0.89 (^[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)))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(848,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[847])).
% 0.96/0.89 tff(849,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(850,plain,
% 0.96/0.89 (^[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))))),
% 0.96/0.89 inference(bind,[status(th)],[])).
% 0.96/0.89 tff(851,plain,
% 0.96/0.89 (![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))),
% 0.96/0.89 inference(quant_intro,[status(thm)],[850])).
% 0.96/0.89 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')).
% 0.96/0.89 tff(853,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.96/0.89 tff(854,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[853, 849])).
% 0.96/0.89 tff(855,plain,(
% 0.96/0.89 ![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.96/0.89 inference(skolemize,[status(sab)],[854])).
% 0.96/0.89 tff(856,plain,
% 0.96/0.89 (![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[855, 848])).
% 0.96/0.89 tff(857,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(858,plain,
% 0.96/0.89 (((~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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(859,plain,
% 0.96/0.89 (((~![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))))),
% 0.96/0.89 inference(monotonicity,[status(thm)],[858])).
% 0.96/0.89 tff(860,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(transitivity,[status(thm)],[859, 857])).
% 0.96/0.89 tff(861,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(862,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.96/0.89 tff(863,plain,
% 0.96/0.89 (m_main_v_state1(s5, c_t1)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[862, 856, 656, 825])).
% 0.96/0.89 tff(864,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.89 inference(rewrite,[status(thm)],[])).
% 0.96/0.89 tff(865,plain,
% 0.96/0.89 ((~![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)))),
% 0.96/0.89 inference(quant_inst,[status(thm)],[])).
% 0.96/0.89 tff(866,plain,
% 0.96/0.89 ((~![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))),
% 0.96/0.89 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.96/0.89 tff(867,plain,
% 0.96/0.89 (~m_main_v_state2(s5, c_t2)),
% 0.96/0.89 inference(unit_resolution,[status(thm)],[866, 77, 734])).
% 0.96/0.89 tff(868,plain,
% 0.96/0.89 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(869,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s5, c_t2) | (~node1(s5)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(870,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s5, c_t2) | (~node1(s5))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.96/0.90 tff(871,plain,
% 0.96/0.90 (~node1(s5)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[870, 195, 867])).
% 0.96/0.90 tff(872,plain,
% 0.96/0.90 (succ(s5, s6) <=> succ(s5, s6)),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(873,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 0.96/0.90 tff(874,plain,
% 0.96/0.90 (succ(s5, s6)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.96/0.90 tff(875,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(876,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(877,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.96/0.90 tff(878,plain,
% 0.96/0.90 (trans(s5, s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[877, 874, 39])).
% 0.96/0.90 tff(879,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(880,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s5, s6)) | node7(s5, s6))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(881,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s5, s6)) | node7(s5, s6)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.96/0.90 tff(882,plain,
% 0.96/0.90 (node7(s5, s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[881, 206, 878])).
% 0.96/0.90 tff(883,plain,
% 0.96/0.90 (^[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)))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(884,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[883])).
% 0.96/0.90 tff(885,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(886,plain,
% 0.96/0.90 (^[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))))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(887,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[886])).
% 0.96/0.90 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')).
% 0.96/0.90 tff(889,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.96/0.90 tff(890,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[889, 885])).
% 0.96/0.90 tff(891,plain,(
% 0.96/0.90 ![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))),
% 0.96/0.90 inference(skolemize,[status(sab)],[890])).
% 0.96/0.90 tff(892,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.96/0.90 tff(893,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(894,plain,
% 0.96/0.90 (((~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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(895,plain,
% 0.96/0.90 (((~![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))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[894])).
% 0.96/0.90 tff(896,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[895, 893])).
% 0.96/0.90 tff(897,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(898,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.96/0.90 tff(899,plain,
% 0.96/0.90 ((~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)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[898, 892, 882])).
% 0.96/0.90 tff(900,plain,
% 0.96/0.90 (m_main_v_state1(s6, c_c1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[899, 871, 734, 863, 846, 742])).
% 0.96/0.90 tff(901,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(902,plain,
% 0.96/0.90 ((~![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)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(903,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.96/0.90 tff(904,plain,
% 0.96/0.90 (~m_main_v_state1(s6, c_t1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[903, 539, 900])).
% 0.96/0.90 tff(905,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(906,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s6, c_t1) | (~node5(s6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(907,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s6, c_t1) | (~node5(s6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.96/0.90 tff(908,plain,
% 0.96/0.90 (~node5(s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[907, 550, 904])).
% 0.96/0.90 tff(909,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(910,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s5, s6)) | node14(s5, s6))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(911,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s5, s6)) | node14(s5, s6)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.96/0.90 tff(912,plain,
% 0.96/0.90 (node14(s5, s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[911, 7, 878])).
% 0.96/0.90 tff(913,plain,
% 0.96/0.90 (^[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)))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(914,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[913])).
% 0.96/0.90 tff(915,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(916,plain,
% 0.96/0.90 (^[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))))),
% 0.96/0.90 inference(bind,[status(th)],[])).
% 0.96/0.90 tff(917,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(quant_intro,[status(thm)],[916])).
% 0.96/0.90 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')).
% 0.96/0.90 tff(919,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.96/0.90 tff(920,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[919, 915])).
% 0.96/0.90 tff(921,plain,(
% 0.96/0.90 ![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))),
% 0.96/0.90 inference(skolemize,[status(sab)],[920])).
% 0.96/0.90 tff(922,plain,
% 0.96/0.90 (![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[921, 914])).
% 0.96/0.90 tff(923,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(924,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(925,plain,
% 0.96/0.90 ((~![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)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.96/0.90 tff(926,plain,
% 0.96/0.90 ((~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_state2(s6, c_t2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[925, 922, 912])).
% 0.96/0.90 tff(927,plain,
% 0.96/0.90 (m_main_v_state2(s6, c_t2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[926, 863, 734])).
% 0.96/0.90 tff(928,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(929,plain,
% 0.96/0.90 ((~![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)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(930,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.96/0.90 tff(931,plain,
% 0.96/0.90 (~m_main_v_state2(s6, c_n2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[930, 77, 927])).
% 0.96/0.90 tff(932,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(933,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s6, c_n2) | (~node4(s6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(934,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s6, c_n2) | (~node4(s6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.96/0.90 tff(935,plain,
% 0.96/0.90 (~node4(s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[934, 388, 931])).
% 0.96/0.90 tff(936,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(937,plain,
% 0.96/0.90 ((~![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)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(938,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.96/0.90 tff(939,plain,
% 0.96/0.90 (~m_main_v_state2(s6, c_c2)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[938, 260, 927])).
% 0.96/0.90 tff(940,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(941,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s6, c_c2) | (~node3(s6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(942,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s6, c_c2) | (~node3(s6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.96/0.90 tff(943,plain,
% 0.96/0.90 (~node3(s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[942, 399, 939])).
% 0.96/0.90 tff(944,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(945,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s6, c_n2) | (~node2(s6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(946,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s6, c_n2) | (~node2(s6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.96/0.90 tff(947,plain,
% 0.96/0.90 (~node2(s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[946, 410, 931])).
% 0.96/0.90 tff(948,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(949,plain,
% 0.96/0.90 ((~![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)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(950,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.96/0.90 tff(951,plain,
% 0.96/0.90 (~m_main_v_state1(s6, c_n1)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[950, 454, 900])).
% 0.96/0.90 tff(952,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(953,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s6, c_n1) | (~node1(s6)))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(954,plain,
% 0.96/0.90 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s6, c_n1) | (~node1(s6))),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.96/0.90 tff(955,plain,
% 0.96/0.90 (~node1(s6)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[954, 421, 951])).
% 0.96/0.90 tff(956,plain,
% 0.96/0.90 (succ(s6, s7) <=> succ(s6, s7)),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(957,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 0.96/0.90 tff(958,plain,
% 0.96/0.90 (succ(s6, s7)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.96/0.90 tff(959,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(960,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(961,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.96/0.90 tff(962,plain,
% 0.96/0.90 (trans(s6, s7)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[961, 958, 39])).
% 0.96/0.90 tff(963,plain,
% 0.96/0.90 (((~![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))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(964,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s6, s7)) | node7(s6, s7))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(965,plain,
% 0.96/0.90 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s6, s7)) | node7(s6, s7)),
% 0.96/0.90 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.96/0.90 tff(966,plain,
% 0.96/0.90 (node7(s6, s7)),
% 0.96/0.90 inference(unit_resolution,[status(thm)],[965, 206, 962])).
% 0.96/0.90 tff(967,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(968,plain,
% 0.96/0.90 (((~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)))),
% 0.96/0.90 inference(rewrite,[status(thm)],[])).
% 0.96/0.90 tff(969,plain,
% 0.96/0.90 (((~![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))))),
% 0.96/0.90 inference(monotonicity,[status(thm)],[968])).
% 0.96/0.90 tff(970,plain,
% 0.96/0.90 (((~![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)))),
% 0.96/0.90 inference(transitivity,[status(thm)],[969, 967])).
% 0.96/0.90 tff(971,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.90 inference(quant_inst,[status(thm)],[])).
% 0.96/0.90 tff(972,plain,
% 0.96/0.90 ((~![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.96/0.91 tff(973,plain,
% 0.96/0.91 (m_main_v_state1(s7, c_n1) | (~m_main_v_state1(s6, c_c1)) | node1(s6) | node2(s6) | node3(s6) | node4(s6) | node5(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[972, 584, 966])).
% 0.96/0.91 tff(974,plain,
% 0.96/0.91 (m_main_v_state1(s7, c_n1)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[973, 955, 900, 947, 943, 935, 908])).
% 0.96/0.91 tff(975,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(976,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s5, c_t2) | (~node15(s5)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(977,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s5, c_t2) | (~node15(s5))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.96/0.91 tff(978,plain,
% 0.96/0.91 (~node15(s5)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[977, 103, 867])).
% 0.96/0.91 tff(979,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(980,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s5, s6)) | node18(s5, s6))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(981,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s5, s6)) | node18(s5, s6)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.96/0.91 tff(982,plain,
% 0.96/0.91 (node18(s5, s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[981, 125, 878])).
% 0.96/0.91 tff(983,plain,
% 0.96/0.91 (^[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)))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(984,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[983])).
% 0.96/0.91 tff(985,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(986,plain,
% 0.96/0.91 (^[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))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(987,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[986])).
% 0.96/0.91 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')).
% 0.96/0.91 tff(989,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.96/0.91 tff(990,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.96/0.91 tff(991,plain,(
% 0.96/0.91 ![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))),
% 0.96/0.91 inference(skolemize,[status(sab)],[990])).
% 0.96/0.91 tff(992,plain,
% 0.96/0.91 (![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[991, 984])).
% 0.96/0.91 tff(993,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(994,plain,
% 0.96/0.91 (((~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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(995,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[994])).
% 0.96/0.91 tff(996,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(transitivity,[status(thm)],[995, 993])).
% 0.96/0.91 tff(997,plain,
% 0.96/0.91 ((~![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))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(998,plain,
% 0.96/0.91 ((~![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)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.96/0.91 tff(999,plain,
% 0.96/0.91 (node15(s5) | (~m_main_v_state1(s5, c_t1)) | (~m_main_v_state2(s5, c_n2)) | m_main_v_turn(s6, c_1)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[998, 992, 982])).
% 0.96/0.91 tff(1000,plain,
% 0.96/0.91 (m_main_v_turn(s6, c_1)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[999, 978, 734, 863])).
% 0.96/0.91 tff(1001,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1002,plain,
% 0.96/0.91 ((~![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)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1003,plain,
% 0.96/0.91 ((~![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.96/0.91 tff(1004,plain,
% 0.96/0.91 (~m_main_v_turn(s6, c_2)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1003, 156, 1000])).
% 0.96/0.91 tff(1005,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1006,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s6, c_2) | (~node12(s6)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1007,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s6, c_2) | (~node12(s6))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.96/0.91 tff(1008,plain,
% 0.96/0.91 (~node12(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1007, 184, 1004])).
% 0.96/0.91 tff(1009,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1010,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s6, c_n2) | (~node8(s6)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1011,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s6, c_n2) | (~node8(s6))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.96/0.91 tff(1012,plain,
% 0.96/0.91 (~node8(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1011, 271, 931])).
% 0.96/0.91 tff(1013,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1014,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s6, c_n2) | (~node9(s6)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1015,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s6, c_n2) | (~node9(s6))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.96/0.91 tff(1016,plain,
% 0.96/0.91 (~node9(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1015, 88, 931])).
% 0.96/0.91 tff(1017,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1018,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s6, c_n2) | (~node10(s6)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1019,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s6, c_n2) | (~node10(s6))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.96/0.91 tff(1020,plain,
% 0.96/0.91 (~node10(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1019, 249, 931])).
% 0.96/0.91 tff(1021,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1022,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s6, c_n1) | (~node11(s6)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1023,plain,
% 0.96/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s6, c_n1) | (~node11(s6))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.96/0.91 tff(1024,plain,
% 0.96/0.91 (~node11(s6)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1023, 238, 951])).
% 0.96/0.91 tff(1025,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1026,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s6, s7)) | node14(s6, s7))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1027,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s6, s7)) | node14(s6, s7)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.96/0.91 tff(1028,plain,
% 0.96/0.91 (node14(s6, s7)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1027, 7, 962])).
% 0.96/0.91 tff(1029,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1030,plain,
% 0.96/0.91 ((~![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)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1031,plain,
% 0.96/0.91 ((~![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))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.96/0.91 tff(1032,plain,
% 0.96/0.91 (m_main_v_state2(s6, c_c2) | node9(s6) | node8(s6) | node10(s6) | node11(s6) | node12(s6) | node13(s6, s7)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1031, 296, 1028])).
% 0.96/0.91 tff(1033,plain,
% 0.96/0.91 (node13(s6, s7)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1032, 1024, 939, 1020, 1016, 1012, 1008])).
% 0.96/0.91 tff(1034,plain,
% 0.96/0.91 (((~![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(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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1035,plain,
% 0.96/0.91 (((~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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1036,plain,
% 0.96/0.91 (((~![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))))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[1035])).
% 0.96/0.91 tff(1037,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.96/0.91 tff(1038,plain,
% 0.96/0.91 ((~![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))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1039,plain,
% 0.96/0.91 ((~![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(s6, c_t2)) | m_main_v_state2(s7, c_t2) | (~node13(s6, s7))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.96/0.91 tff(1040,plain,
% 0.96/0.91 (m_main_v_state2(s7, c_t2)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1039, 518, 927, 1033])).
% 0.96/0.91 tff(1041,plain,
% 0.96/0.91 (succ(s7, s8) <=> succ(s7, s8)),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1042,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 0.96/0.91 tff(1043,plain,
% 0.96/0.91 (succ(s7, s8)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.96/0.91 tff(1044,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1045,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1046,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.96/0.91 tff(1047,plain,
% 0.96/0.91 (trans(s7, s8)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1046, 1043, 39])).
% 0.96/0.91 tff(1048,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1049,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s7, s8)) | node7(s7, s8))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1050,plain,
% 0.96/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s7, s8)) | node7(s7, s8)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.96/0.91 tff(1051,plain,
% 0.96/0.91 (node7(s7, s8)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1050, 206, 1047])).
% 0.96/0.91 tff(1052,plain,
% 0.96/0.91 (((~![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))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1053,plain,
% 0.96/0.91 ((~![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))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1054,plain,
% 0.96/0.91 ((~![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)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.96/0.91 tff(1055,plain,
% 0.96/0.91 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_state1(s8, c_t1)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1054, 651, 1051])).
% 0.96/0.91 tff(1056,plain,
% 0.96/0.91 (m_main_v_state1(s8, c_t1)),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[1055, 1040, 974])).
% 0.96/0.91 tff(1057,plain,
% 0.96/0.91 (((~![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(1058,plain,
% 0.96/0.91 ((~![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)))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(1059,plain,
% 1.00/0.91 ((~![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))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 1.00/0.91 tff(1060,plain,
% 1.00/0.91 (~m_main_v_state1(s8, c_n1)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1059, 17, 1056])).
% 1.00/0.91 tff(1061,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1062,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s8, c_n1) | (~node1(s8)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1063,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s8, c_n1) | (~node1(s8))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.00/0.91 tff(1064,plain,
% 1.00/0.91 (~node1(s8)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1063, 421, 1060])).
% 1.00/0.91 tff(1065,plain,
% 1.00/0.91 (((~![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))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1066,plain,
% 1.00/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s7, s8)) | node18(s7, s8))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1067,plain,
% 1.00/0.91 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s7, s8)) | node18(s7, s8)),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 1.00/0.91 tff(1068,plain,
% 1.00/0.91 (node18(s7, s8)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1067, 125, 1047])).
% 1.00/0.91 tff(1069,plain,
% 1.00/0.91 (((~![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))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1070,plain,
% 1.00/0.91 ((~![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))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1071,plain,
% 1.00/0.91 ((~![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)),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.00/0.91 tff(1072,plain,
% 1.00/0.91 ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state2(s7, c_t2)) | m_main_v_turn(s8, c_2)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1071, 760, 1068])).
% 1.00/0.91 tff(1073,plain,
% 1.00/0.91 (m_main_v_turn(s8, c_2)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1072, 1040, 974])).
% 1.00/0.91 tff(1074,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1075,plain,
% 1.00/0.91 ((~![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)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1076,plain,
% 1.00/0.91 ((~![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))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.00/0.91 tff(1077,plain,
% 1.00/0.91 (~m_main_v_turn(s8, c_1)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1076, 156, 1073])).
% 1.00/0.91 tff(1078,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1079,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s8, c_1) | (~node5(s8)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1080,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s8, c_1) | (~node5(s8))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.00/0.91 tff(1081,plain,
% 1.00/0.91 (~node5(s8)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1080, 776, 1077])).
% 1.00/0.91 tff(1082,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1083,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s8, c_n1) | (~node2(s8)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1084,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s8, c_n1) | (~node2(s8))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.00/0.91 tff(1085,plain,
% 1.00/0.91 (~node2(s8)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1084, 787, 1060])).
% 1.00/0.91 tff(1086,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1087,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s8, c_n1) | (~node3(s8)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1088,plain,
% 1.00/0.91 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s8, c_n1) | (~node3(s8))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.00/0.91 tff(1089,plain,
% 1.00/0.91 (~node3(s8)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1088, 798, 1060])).
% 1.00/0.91 tff(1090,plain,
% 1.00/0.91 (((~![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)))),
% 1.00/0.91 inference(rewrite,[status(thm)],[])).
% 1.00/0.91 tff(1091,plain,
% 1.00/0.91 ((~![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)))),
% 1.00/0.91 inference(quant_inst,[status(thm)],[])).
% 1.00/0.91 tff(1092,plain,
% 1.00/0.91 ((~![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))),
% 1.00/0.91 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.00/0.91 tff(1093,plain,
% 1.00/0.91 (~m_main_v_state1(s8, c_c1)),
% 1.00/0.91 inference(unit_resolution,[status(thm)],[1092, 539, 1056])).
% 1.00/0.91 tff(1094,plain,
% 1.00/0.91 (((~![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(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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1095,plain,
% 1.00/0.92 (((~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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1096,plain,
% 1.00/0.92 (((~![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))))),
% 1.00/0.92 inference(monotonicity,[status(thm)],[1095])).
% 1.00/0.92 tff(1097,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(transitivity,[status(thm)],[1096, 1094])).
% 1.00/0.92 tff(1098,plain,
% 1.00/0.92 ((~![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)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1099,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 1.00/0.92 tff(1100,plain,
% 1.00/0.92 (~m_main_v_state2(s7, c_n2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1099, 311, 931, 1033])).
% 1.00/0.92 tff(1101,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1102,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s7, c_n2) | (~node9(s7)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1103,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s7, c_n2) | (~node9(s7))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.00/0.92 tff(1104,plain,
% 1.00/0.92 (~node9(s7)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1103, 88, 1100])).
% 1.00/0.92 tff(1105,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1106,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s7, c_n2) | (~node10(s7)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1107,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s7, c_n2) | (~node10(s7))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.00/0.92 tff(1108,plain,
% 1.00/0.92 (~node10(s7)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1107, 249, 1100])).
% 1.00/0.92 tff(1109,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1110,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s7, c_n2) | (~node8(s7)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1111,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s7, c_n2) | (~node8(s7))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 1.00/0.92 tff(1112,plain,
% 1.00/0.92 (~node8(s7)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1111, 271, 1100])).
% 1.00/0.92 tff(1113,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1114,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s7, s8)) | node14(s7, s8))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1115,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s7, s8)) | node14(s7, s8)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.00/0.92 tff(1116,plain,
% 1.00/0.92 (node14(s7, s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1115, 7, 1047])).
% 1.00/0.92 tff(1117,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1118,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1119,plain,
% 1.00/0.92 ((~![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)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.00/0.92 tff(1120,plain,
% 1.00/0.92 ((~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)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1119, 617, 1116])).
% 1.00/0.92 tff(1121,plain,
% 1.00/0.92 (m_main_v_state2(s8, c_c2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1120, 1112, 974, 1040, 1108, 1104])).
% 1.00/0.92 tff(1122,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1123,plain,
% 1.00/0.92 ((~![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)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1124,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.00/0.92 tff(1125,plain,
% 1.00/0.92 (~m_main_v_state2(s8, c_n2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1124, 697, 1121])).
% 1.00/0.92 tff(1126,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1127,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s8, c_n2) | (~node4(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1128,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s8, c_n2) | (~node4(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.00/0.92 tff(1129,plain,
% 1.00/0.92 (~node4(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1128, 388, 1125])).
% 1.00/0.92 tff(1130,plain,
% 1.00/0.92 (succ(s8, s9) <=> succ(s8, s9)),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1131,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 1.00/0.92 tff(1132,plain,
% 1.00/0.92 (succ(s8, s9)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.00/0.92 tff(1133,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1134,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1135,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.00/0.92 tff(1136,plain,
% 1.00/0.92 (trans(s8, s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1135, 1132, 39])).
% 1.00/0.92 tff(1137,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1138,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s8, s9)) | node7(s8, s9))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1139,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s8, s9)) | node7(s8, s9)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.00/0.92 tff(1140,plain,
% 1.00/0.92 (node7(s8, s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1139, 206, 1136])).
% 1.00/0.92 tff(1141,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1142,plain,
% 1.00/0.92 ((~![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)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1143,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.00/0.92 tff(1144,plain,
% 1.00/0.92 (m_main_v_state1(s8, c_c1) | node1(s8) | node2(s8) | node3(s8) | node4(s8) | node5(s8) | node6(s8, s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1143, 820, 1140])).
% 1.00/0.92 tff(1145,plain,
% 1.00/0.92 (node6(s8, s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1144, 1129, 1093, 1089, 1085, 1081, 1064])).
% 1.00/0.92 tff(1146,plain,
% 1.00/0.92 (((~![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(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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1147,plain,
% 1.00/0.92 (((~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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1148,plain,
% 1.00/0.92 (((~![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))))),
% 1.00/0.92 inference(monotonicity,[status(thm)],[1147])).
% 1.00/0.92 tff(1149,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.00/0.92 tff(1150,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1151,plain,
% 1.00/0.92 ((~![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(s8, c_t1)) | m_main_v_state1(s9, c_t1) | (~node6(s8, s9))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.00/0.92 tff(1152,plain,
% 1.00/0.92 (m_main_v_state1(s9, c_t1)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1151, 856, 1056, 1145])).
% 1.00/0.92 tff(1153,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1154,plain,
% 1.00/0.92 ((~![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)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1155,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.00/0.92 tff(1156,plain,
% 1.00/0.92 (~m_main_v_state2(s8, c_t2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1155, 260, 1121])).
% 1.00/0.92 tff(1157,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1158,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s8, c_t2) | (~node12(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1159,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s8, c_t2) | (~node12(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 1.00/0.92 tff(1160,plain,
% 1.00/0.92 (~node12(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1159, 633, 1156])).
% 1.00/0.92 tff(1161,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1162,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s8, c_n1) | (~node11(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1163,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s8, c_n1) | (~node11(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 1.00/0.92 tff(1164,plain,
% 1.00/0.92 (~node11(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1163, 238, 1060])).
% 1.00/0.92 tff(1165,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1166,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s8, c_c1) | (~node10(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1167,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s8, c_c1) | (~node10(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.00/0.92 tff(1168,plain,
% 1.00/0.92 (~node10(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1167, 675, 1093])).
% 1.00/0.92 tff(1169,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1170,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s8, c_n1) | (~node9(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1171,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s8, c_n1) | (~node9(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.00/0.92 tff(1172,plain,
% 1.00/0.92 (~node9(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1171, 686, 1060])).
% 1.00/0.92 tff(1173,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1174,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s8, c_n2) | (~node8(s8)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1175,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s8, c_n2) | (~node8(s8))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 1.00/0.92 tff(1176,plain,
% 1.00/0.92 (~node8(s8)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1175, 271, 1125])).
% 1.00/0.92 tff(1177,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1178,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s8, s9)) | node14(s8, s9))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1179,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s8, s9)) | node14(s8, s9)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.00/0.92 tff(1180,plain,
% 1.00/0.92 (node14(s8, s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1179, 7, 1136])).
% 1.00/0.92 tff(1181,plain,
% 1.00/0.92 (((~![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(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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1182,plain,
% 1.00/0.92 (((~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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1183,plain,
% 1.00/0.92 (((~![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(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))))),
% 1.00/0.92 inference(monotonicity,[status(thm)],[1182])).
% 1.00/0.92 tff(1184,plain,
% 1.00/0.92 (((~![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(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)))),
% 1.00/0.92 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.00/0.92 tff(1185,plain,
% 1.00/0.92 ((~![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(s8, c_c2)) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | m_main_v_state2(s9, c_n2))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1186,plain,
% 1.00/0.92 ((~![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(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~node14(s8, s9)) | (~m_main_v_state2(s8, c_c2))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.00/0.92 tff(1187,plain,
% 1.00/0.92 (m_main_v_state2(s9, c_n2) | node9(s8) | node8(s8) | node10(s8) | node11(s8) | node12(s8) | (~m_main_v_state2(s8, c_c2))),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1186, 726, 1180])).
% 1.00/0.92 tff(1188,plain,
% 1.00/0.92 (m_main_v_state2(s9, c_n2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1187, 1176, 1121, 1172, 1168, 1164, 1160])).
% 1.00/0.92 tff(1189,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1190,plain,
% 1.00/0.92 ((~![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)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1191,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.00/0.92 tff(1192,plain,
% 1.00/0.92 (~m_main_v_state2(s9, c_t2)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1191, 77, 1188])).
% 1.00/0.92 tff(1193,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1194,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s9, c_t2) | (~node15(s9)))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1195,plain,
% 1.00/0.92 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s9, c_t2) | (~node15(s9))),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.00/0.92 tff(1196,plain,
% 1.00/0.92 (~node15(s9)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1195, 103, 1192])).
% 1.00/0.92 tff(1197,plain,
% 1.00/0.92 (succ(s9, s10) <=> succ(s9, s10)),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1198,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 1.00/0.92 tff(1199,plain,
% 1.00/0.92 (succ(s9, s10)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.00/0.92 tff(1200,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1201,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1202,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.00/0.92 tff(1203,plain,
% 1.00/0.92 (trans(s9, s10)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1202, 1199, 39])).
% 1.00/0.92 tff(1204,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1205,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s9, s10)) | node18(s9, s10))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1206,plain,
% 1.00/0.92 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s9, s10)) | node18(s9, s10)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 1.00/0.92 tff(1207,plain,
% 1.00/0.92 (node18(s9, s10)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1206, 125, 1203])).
% 1.00/0.92 tff(1208,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1209,plain,
% 1.00/0.92 (((~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))),
% 1.00/0.92 inference(rewrite,[status(thm)],[])).
% 1.00/0.92 tff(1210,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.92 inference(monotonicity,[status(thm)],[1209])).
% 1.00/0.92 tff(1211,plain,
% 1.00/0.92 (((~![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))),
% 1.00/0.92 inference(transitivity,[status(thm)],[1210, 1208])).
% 1.00/0.92 tff(1212,plain,
% 1.00/0.92 ((~![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))),
% 1.00/0.92 inference(quant_inst,[status(thm)],[])).
% 1.00/0.92 tff(1213,plain,
% 1.00/0.92 ((~![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)),
% 1.00/0.92 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 1.00/0.92 tff(1214,plain,
% 1.00/0.92 (node15(s9) | (~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_turn(s10, c_1)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1213, 992, 1207])).
% 1.00/0.92 tff(1215,plain,
% 1.00/0.92 (m_main_v_turn(s10, c_1)),
% 1.00/0.92 inference(unit_resolution,[status(thm)],[1214, 1196, 1188, 1152])).
% 1.00/0.92 tff(1216,plain,
% 1.00/0.92 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1217,plain,
% 1.00/0.93 ((~![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)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1218,plain,
% 1.00/0.93 ((~![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))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 1.00/0.93 tff(1219,plain,
% 1.00/0.93 (~m_main_v_turn(s10, c_2)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1218, 156, 1215])).
% 1.00/0.93 tff(1220,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1221,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s10, c_2) | (~node12(s10)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1222,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s10, c_2) | (~node12(s10))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.00/0.93 tff(1223,plain,
% 1.00/0.93 (~node12(s10)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1222, 184, 1219])).
% 1.00/0.93 tff(1224,plain,
% 1.00/0.93 (((~![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))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1225,plain,
% 1.00/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s9, s10)) | node14(s9, s10))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1226,plain,
% 1.00/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s9, s10)) | node14(s9, s10)),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 1.00/0.93 tff(1227,plain,
% 1.00/0.93 (node14(s9, s10)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1226, 7, 1203])).
% 1.00/0.93 tff(1228,plain,
% 1.00/0.93 (((~![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(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))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1229,plain,
% 1.00/0.93 ((~![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(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1230,plain,
% 1.00/0.93 ((~![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(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | (~node14(s9, s10)) | m_main_v_state2(s10, c_t2)),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 1.00/0.93 tff(1231,plain,
% 1.00/0.93 ((~m_main_v_state1(s9, c_t1)) | (~m_main_v_state2(s9, c_n2)) | m_main_v_state2(s10, c_t2)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1230, 922, 1227])).
% 1.00/0.93 tff(1232,plain,
% 1.00/0.93 (m_main_v_state2(s10, c_t2)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1231, 1152, 1188])).
% 1.00/0.93 tff(1233,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1234,plain,
% 1.00/0.93 ((~![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)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1235,plain,
% 1.00/0.93 ((~![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))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.00/0.93 tff(1236,plain,
% 1.00/0.93 (~m_main_v_state2(s10, c_n2)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1235, 77, 1232])).
% 1.00/0.93 tff(1237,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1238,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s10, c_n2) | (~node8(s10)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1239,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s10, c_n2) | (~node8(s10))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.00/0.93 tff(1240,plain,
% 1.00/0.93 (~node8(s10)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1239, 271, 1236])).
% 1.00/0.93 tff(1241,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1242,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s10, c_n2) | (~node9(s10)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1243,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s10, c_n2) | (~node9(s10))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 1.00/0.93 tff(1244,plain,
% 1.00/0.93 (~node9(s10)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1243, 88, 1236])).
% 1.00/0.93 tff(1245,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1246,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s10, c_n2) | (~node10(s10)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1247,plain,
% 1.00/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s10, c_n2) | (~node10(s10))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 1.00/0.93 tff(1248,plain,
% 1.00/0.93 (~node10(s10)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1247, 249, 1236])).
% 1.00/0.93 tff(1249,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1250,plain,
% 1.00/0.93 ((~![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)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1251,plain,
% 1.00/0.93 ((~![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))),
% 1.00/0.93 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.00/0.93 tff(1252,plain,
% 1.00/0.93 (~m_main_v_state2(s10, c_c2)),
% 1.00/0.93 inference(unit_resolution,[status(thm)],[1251, 260, 1232])).
% 1.00/0.93 tff(1253,plain,
% 1.00/0.93 (((~![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)))),
% 1.00/0.93 inference(rewrite,[status(thm)],[])).
% 1.00/0.93 tff(1254,plain,
% 1.00/0.93 ((~![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)))),
% 1.00/0.93 inference(quant_inst,[status(thm)],[])).
% 1.00/0.93 tff(1255,plain,
% 1.00/0.93 ((~![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))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.01/0.93 tff(1256,plain,
% 1.01/0.93 (~m_main_v_state2(s9, c_c2)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1255, 697, 1188])).
% 1.01/0.93 tff(1257,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1258,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s9, c_c2) | (~node3(s9)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1259,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s9, c_c2) | (~node3(s9))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.01/0.93 tff(1260,plain,
% 1.01/0.93 (~node3(s9)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1259, 399, 1256])).
% 1.01/0.93 tff(1261,plain,
% 1.01/0.93 (((~![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(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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1262,plain,
% 1.01/0.93 (((~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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1263,plain,
% 1.01/0.93 (((~![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))))),
% 1.01/0.93 inference(monotonicity,[status(thm)],[1262])).
% 1.01/0.93 tff(1264,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(transitivity,[status(thm)],[1263, 1261])).
% 1.01/0.93 tff(1265,plain,
% 1.01/0.93 ((~![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)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1266,plain,
% 1.01/0.93 ((~![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(s8, c_n1) | (~m_main_v_state1(s9, c_n1)) | (~node6(s8, s9))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.01/0.93 tff(1267,plain,
% 1.01/0.93 (~m_main_v_state1(s9, c_n1)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1266, 835, 1060, 1145])).
% 1.01/0.93 tff(1268,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1269,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s9, c_n1) | (~node2(s9)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1270,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s9, c_n1) | (~node2(s9))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.01/0.93 tff(1271,plain,
% 1.01/0.93 (~node2(s9)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1270, 787, 1267])).
% 1.01/0.93 tff(1272,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1273,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s9, c_t2) | (~node1(s9)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1274,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s9, c_t2) | (~node1(s9))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 1.01/0.93 tff(1275,plain,
% 1.01/0.93 (~node1(s9)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1274, 195, 1192])).
% 1.01/0.93 tff(1276,plain,
% 1.01/0.93 (((~![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))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1277,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s9, s10)) | node7(s9, s10))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1278,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s9, s10)) | node7(s9, s10)),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 1.01/0.93 tff(1279,plain,
% 1.01/0.93 (node7(s9, s10)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1278, 206, 1203])).
% 1.01/0.93 tff(1280,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1281,plain,
% 1.01/0.93 (((~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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1282,plain,
% 1.01/0.93 (((~![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))))),
% 1.01/0.93 inference(monotonicity,[status(thm)],[1281])).
% 1.01/0.93 tff(1283,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(transitivity,[status(thm)],[1282, 1280])).
% 1.01/0.93 tff(1284,plain,
% 1.01/0.93 ((~![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))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1285,plain,
% 1.01/0.93 ((~![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))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.01/0.93 tff(1286,plain,
% 1.01/0.93 ((~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)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1285, 892, 1279])).
% 1.01/0.93 tff(1287,plain,
% 1.01/0.93 (m_main_v_state1(s10, c_c1)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1286, 1275, 1188, 1152, 1271, 1260])).
% 1.01/0.93 tff(1288,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1289,plain,
% 1.01/0.93 ((~![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)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1290,plain,
% 1.01/0.93 ((~![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))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.01/0.93 tff(1291,plain,
% 1.01/0.93 (~m_main_v_state1(s10, c_n1)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1290, 454, 1287])).
% 1.01/0.93 tff(1292,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1293,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s10, c_n1) | (~node11(s10)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1294,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s10, c_n1) | (~node11(s10))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.01/0.93 tff(1295,plain,
% 1.01/0.93 (~node11(s10)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1294, 238, 1291])).
% 1.01/0.93 tff(1296,plain,
% 1.01/0.93 (succ(s10, s11) <=> succ(s10, s11)),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1297,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 1.01/0.93 tff(1298,plain,
% 1.01/0.93 (succ(s10, s11)),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.01/0.93 tff(1299,plain,
% 1.01/0.93 (((~![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))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1300,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1301,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.01/0.93 tff(1302,plain,
% 1.01/0.93 (trans(s10, s11)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1301, 1298, 39])).
% 1.01/0.93 tff(1303,plain,
% 1.01/0.93 (((~![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))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1304,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s10, s11)) | node14(s10, s11))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1305,plain,
% 1.01/0.93 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s10, s11)) | node14(s10, s11)),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.01/0.93 tff(1306,plain,
% 1.01/0.93 (node14(s10, s11)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1305, 7, 1302])).
% 1.01/0.93 tff(1307,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1308,plain,
% 1.01/0.93 ((~![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)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1309,plain,
% 1.01/0.93 ((~![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))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 1.01/0.93 tff(1310,plain,
% 1.01/0.93 (m_main_v_state2(s10, c_c2) | node9(s10) | node8(s10) | node10(s10) | node11(s10) | node12(s10) | node13(s10, s11)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1309, 296, 1306])).
% 1.01/0.93 tff(1311,plain,
% 1.01/0.93 (node13(s10, s11)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1310, 1295, 1252, 1248, 1244, 1240, 1223])).
% 1.01/0.93 tff(1312,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1313,plain,
% 1.01/0.93 (((~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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1314,plain,
% 1.01/0.93 (((~![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))))),
% 1.01/0.93 inference(monotonicity,[status(thm)],[1313])).
% 1.01/0.93 tff(1315,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.01/0.93 tff(1316,plain,
% 1.01/0.93 ((~![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)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1317,plain,
% 1.01/0.93 ((~![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))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.01/0.93 tff(1318,plain,
% 1.01/0.93 (~m_main_v_state2(s11, c_n2)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1317, 311, 1236, 1311])).
% 1.01/0.93 tff(1319,plain,
% 1.01/0.93 (((~![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)))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1320,plain,
% 1.01/0.93 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s11, c_n2) | (~node9(s11)))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1321,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s11, c_n2) | (~node9(s11))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.01/0.94 tff(1322,plain,
% 1.01/0.94 (~node9(s11)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1321, 88, 1318])).
% 1.01/0.94 tff(1323,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1324,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s11, c_n2) | (~node10(s11)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1325,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s11, c_n2) | (~node10(s11))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.01/0.94 tff(1326,plain,
% 1.01/0.94 (~node10(s11)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1325, 249, 1318])).
% 1.01/0.94 tff(1327,plain,
% 1.01/0.94 (((~![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(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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1328,plain,
% 1.01/0.94 (((~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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1329,plain,
% 1.01/0.94 (((~![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))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1328])).
% 1.01/0.94 tff(1330,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1329, 1327])).
% 1.01/0.94 tff(1331,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1332,plain,
% 1.01/0.94 ((~![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(s10, c_t2)) | m_main_v_state2(s11, c_t2) | (~node13(s10, s11))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 1.01/0.94 tff(1333,plain,
% 1.01/0.94 (m_main_v_state2(s11, c_t2)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1332, 518, 1232, 1311])).
% 1.01/0.94 tff(1334,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1335,plain,
% 1.01/0.94 ((~![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)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1336,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.01/0.94 tff(1337,plain,
% 1.01/0.94 (~m_main_v_state1(s10, c_t1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1336, 539, 1287])).
% 1.01/0.94 tff(1338,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1339,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s10, c_t1) | (~node5(s10)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1340,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s10, c_t1) | (~node5(s10))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 1.01/0.94 tff(1341,plain,
% 1.01/0.94 (~node5(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1340, 550, 1337])).
% 1.01/0.94 tff(1342,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1343,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s10, c_n2) | (~node4(s10)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1344,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s10, c_n2) | (~node4(s10))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.01/0.94 tff(1345,plain,
% 1.01/0.94 (~node4(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1344, 388, 1236])).
% 1.01/0.94 tff(1346,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1347,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s10, c_c2) | (~node3(s10)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1348,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s10, c_c2) | (~node3(s10))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 1.01/0.94 tff(1349,plain,
% 1.01/0.94 (~node3(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1348, 399, 1252])).
% 1.01/0.94 tff(1350,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1351,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s10, c_n2) | (~node2(s10)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1352,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s10, c_n2) | (~node2(s10))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.01/0.94 tff(1353,plain,
% 1.01/0.94 (~node2(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1352, 410, 1236])).
% 1.01/0.94 tff(1354,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1355,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s10, c_n1) | (~node1(s10)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1356,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s10, c_n1) | (~node1(s10))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.01/0.94 tff(1357,plain,
% 1.01/0.94 (~node1(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1356, 421, 1291])).
% 1.01/0.94 tff(1358,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1359,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s10, s11)) | node7(s10, s11))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1360,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s10, s11)) | node7(s10, s11)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.01/0.94 tff(1361,plain,
% 1.01/0.94 (node7(s10, s11)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1360, 206, 1302])).
% 1.01/0.94 tff(1362,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1363,plain,
% 1.01/0.94 (((~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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1364,plain,
% 1.01/0.94 (((~![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))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1363])).
% 1.01/0.94 tff(1365,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1364, 1362])).
% 1.01/0.94 tff(1366,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1367,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.01/0.94 tff(1368,plain,
% 1.01/0.94 (m_main_v_state1(s11, c_n1) | (~m_main_v_state1(s10, c_c1)) | node1(s10) | node2(s10) | node3(s10) | node4(s10) | node5(s10)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1367, 584, 1361])).
% 1.01/0.94 tff(1369,plain,
% 1.01/0.94 (m_main_v_state1(s11, c_n1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1368, 1357, 1287, 1353, 1349, 1345, 1341])).
% 1.01/0.94 tff(1370,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1371,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s11, c_n2) | (~node8(s11)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1372,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s11, c_n2) | (~node8(s11))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 1.01/0.94 tff(1373,plain,
% 1.01/0.94 (~node8(s11)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1372, 271, 1318])).
% 1.01/0.94 tff(1374,plain,
% 1.01/0.94 (succ(s11, s12) <=> succ(s11, s12)),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1375,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 1.01/0.94 tff(1376,plain,
% 1.01/0.94 (succ(s11, s12)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.01/0.94 tff(1377,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1378,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1379,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 1.01/0.94 tff(1380,plain,
% 1.01/0.94 (trans(s11, s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1379, 1376, 39])).
% 1.01/0.94 tff(1381,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1382,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s11, s12)) | node14(s11, s12))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1383,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s11, s12)) | node14(s11, s12)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 1.01/0.94 tff(1384,plain,
% 1.01/0.94 (node14(s11, s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1383, 7, 1380])).
% 1.01/0.94 tff(1385,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1386,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1387,plain,
% 1.01/0.94 ((~![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)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.01/0.94 tff(1388,plain,
% 1.01/0.94 ((~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)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1387, 617, 1384])).
% 1.01/0.94 tff(1389,plain,
% 1.01/0.94 (m_main_v_state2(s12, c_c2)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1388, 1373, 1369, 1333, 1326, 1322])).
% 1.01/0.94 tff(1390,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1391,plain,
% 1.01/0.94 ((~![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)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1392,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.01/0.94 tff(1393,plain,
% 1.01/0.94 (~m_main_v_state2(s12, c_t2)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1392, 260, 1389])).
% 1.01/0.94 tff(1394,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1395,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s12, c_t2) | (~node12(s12)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1396,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s12, c_t2) | (~node12(s12))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.01/0.94 tff(1397,plain,
% 1.01/0.94 (~node12(s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1396, 633, 1393])).
% 1.01/0.94 tff(1398,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1399,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s11, s12)) | node7(s11, s12))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1400,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s11, s12)) | node7(s11, s12)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.01/0.94 tff(1401,plain,
% 1.01/0.94 (node7(s11, s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1400, 206, 1380])).
% 1.01/0.94 tff(1402,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1403,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1404,plain,
% 1.01/0.94 ((~![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)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.01/0.94 tff(1405,plain,
% 1.01/0.94 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_state1(s12, c_t1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1404, 651, 1401])).
% 1.01/0.94 tff(1406,plain,
% 1.01/0.94 (m_main_v_state1(s12, c_t1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1405, 1333, 1369])).
% 1.01/0.94 tff(1407,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1408,plain,
% 1.01/0.94 ((~![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)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1409,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.01/0.94 tff(1410,plain,
% 1.01/0.94 (~m_main_v_state1(s12, c_n1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1409, 17, 1406])).
% 1.01/0.94 tff(1411,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1412,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s12, c_n1) | (~node11(s12)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1413,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s12, c_n1) | (~node11(s12))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 1.01/0.94 tff(1414,plain,
% 1.01/0.94 (~node11(s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1413, 238, 1410])).
% 1.01/0.94 tff(1415,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1416,plain,
% 1.01/0.94 ((~![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)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1417,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 1.01/0.94 tff(1418,plain,
% 1.01/0.94 (~m_main_v_state1(s12, c_c1)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1417, 539, 1406])).
% 1.01/0.94 tff(1419,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1420,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s12, c_c1) | (~node10(s12)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1421,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s12, c_c1) | (~node10(s12))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.01/0.94 tff(1422,plain,
% 1.01/0.94 (~node10(s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1421, 675, 1418])).
% 1.01/0.94 tff(1423,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1424,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s12, c_n1) | (~node9(s12)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1425,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s12, c_n1) | (~node9(s12))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.01/0.94 tff(1426,plain,
% 1.01/0.94 (~node9(s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1425, 686, 1410])).
% 1.01/0.94 tff(1427,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1428,plain,
% 1.01/0.94 ((~![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)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1429,plain,
% 1.01/0.94 ((~![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))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.01/0.94 tff(1430,plain,
% 1.01/0.94 (~m_main_v_state2(s12, c_n2)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1429, 697, 1389])).
% 1.01/0.94 tff(1431,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1432,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s12, c_n2) | (~node8(s12)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1433,plain,
% 1.01/0.94 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s12, c_n2) | (~node8(s12))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.01/0.94 tff(1434,plain,
% 1.01/0.94 (~node8(s12)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1433, 271, 1430])).
% 1.01/0.94 tff(1435,plain,
% 1.01/0.94 (succ(s12, s13) <=> succ(s12, s13)),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1436,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 1.01/0.94 tff(1437,plain,
% 1.01/0.94 (succ(s12, s13)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 1.01/0.94 tff(1438,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1439,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1440,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 1.01/0.94 tff(1441,plain,
% 1.01/0.94 (trans(s12, s13)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1440, 1437, 39])).
% 1.01/0.94 tff(1442,plain,
% 1.01/0.94 (((~![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))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1443,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s12, s13)) | node14(s12, s13))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1444,plain,
% 1.01/0.94 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s12, s13)) | node14(s12, s13)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.01/0.94 tff(1445,plain,
% 1.01/0.94 (node14(s12, s13)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1444, 7, 1441])).
% 1.01/0.94 tff(1446,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1447,plain,
% 1.01/0.94 (((~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)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1448,plain,
% 1.01/0.94 (((~![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))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1447])).
% 1.01/0.94 tff(1449,plain,
% 1.01/0.94 (((~![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)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1448, 1446])).
% 1.01/0.94 tff(1450,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1451,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 1.01/0.95 tff(1452,plain,
% 1.01/0.95 (m_main_v_state2(s13, c_n2) | node9(s12) | node8(s12) | node10(s12) | node11(s12) | node12(s12) | (~m_main_v_state2(s12, c_c2))),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1451, 726, 1445])).
% 1.01/0.95 tff(1453,plain,
% 1.01/0.95 (m_main_v_state2(s13, c_n2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1452, 1434, 1389, 1426, 1422, 1414, 1397])).
% 1.01/0.95 tff(1454,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1455,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1456,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 1.01/0.95 tff(1457,plain,
% 1.01/0.95 (~m_main_v_state2(s13, c_c2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1456, 697, 1453])).
% 1.01/0.95 tff(1458,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1459,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s13, c_c2) | (~node3(s13)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1460,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s13, c_c2) | (~node3(s13))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.01/0.95 tff(1461,plain,
% 1.01/0.95 (~node3(s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1460, 399, 1457])).
% 1.01/0.95 tff(1462,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1463,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s12, c_n1) | (~node1(s12)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1464,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s12, c_n1) | (~node1(s12))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.01/0.95 tff(1465,plain,
% 1.01/0.95 (~node1(s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1464, 421, 1410])).
% 1.01/0.95 tff(1466,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1467,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s11, s12)) | node18(s11, s12))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1468,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s11, s12)) | node18(s11, s12)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.01/0.95 tff(1469,plain,
% 1.01/0.95 (node18(s11, s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1468, 125, 1380])).
% 1.01/0.95 tff(1470,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1471,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1472,plain,
% 1.01/0.95 ((~![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)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 1.01/0.95 tff(1473,plain,
% 1.01/0.95 ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state2(s11, c_t2)) | m_main_v_turn(s12, c_2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1472, 760, 1469])).
% 1.01/0.95 tff(1474,plain,
% 1.01/0.95 (m_main_v_turn(s12, c_2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1473, 1333, 1369])).
% 1.01/0.95 tff(1475,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1476,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1477,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.01/0.95 tff(1478,plain,
% 1.01/0.95 (~m_main_v_turn(s12, c_1)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1477, 156, 1474])).
% 1.01/0.95 tff(1479,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1480,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s12, c_1) | (~node5(s12)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1481,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s12, c_1) | (~node5(s12))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.01/0.95 tff(1482,plain,
% 1.01/0.95 (~node5(s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1481, 776, 1478])).
% 1.01/0.95 tff(1483,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1484,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s12, c_n1) | (~node2(s12)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1485,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s12, c_n1) | (~node2(s12))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.01/0.95 tff(1486,plain,
% 1.01/0.95 (~node2(s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1485, 787, 1410])).
% 1.01/0.95 tff(1487,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1488,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s12, c_n1) | (~node3(s12)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1489,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s12, c_n1) | (~node3(s12))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 1.01/0.95 tff(1490,plain,
% 1.01/0.95 (~node3(s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1489, 798, 1410])).
% 1.01/0.95 tff(1491,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1492,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s12, c_n2) | (~node4(s12)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1493,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s12, c_n2) | (~node4(s12))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.01/0.95 tff(1494,plain,
% 1.01/0.95 (~node4(s12)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1493, 388, 1430])).
% 1.01/0.95 tff(1495,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1496,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s12, s13)) | node7(s12, s13))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1497,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s12, s13)) | node7(s12, s13)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.01/0.95 tff(1498,plain,
% 1.01/0.95 (node7(s12, s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1497, 206, 1441])).
% 1.01/0.95 tff(1499,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1500,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1501,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.01/0.95 tff(1502,plain,
% 1.01/0.95 (m_main_v_state1(s12, c_c1) | node1(s12) | node2(s12) | node3(s12) | node4(s12) | node5(s12) | node6(s12, s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1501, 820, 1498])).
% 1.01/0.95 tff(1503,plain,
% 1.01/0.95 (node6(s12, s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1502, 1494, 1418, 1490, 1486, 1482, 1465])).
% 1.01/0.95 tff(1504,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1505,plain,
% 1.01/0.95 (((~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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1506,plain,
% 1.01/0.95 (((~![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))))),
% 1.01/0.95 inference(monotonicity,[status(thm)],[1505])).
% 1.01/0.95 tff(1507,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(transitivity,[status(thm)],[1506, 1504])).
% 1.01/0.95 tff(1508,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1509,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 1.01/0.95 tff(1510,plain,
% 1.01/0.95 (~m_main_v_state1(s13, c_n1)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1509, 835, 1410, 1503])).
% 1.01/0.95 tff(1511,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1512,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s13, c_n1) | (~node2(s13)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1513,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s13, c_n1) | (~node2(s13))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.01/0.95 tff(1514,plain,
% 1.01/0.95 (~node2(s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1513, 787, 1510])).
% 1.01/0.95 tff(1515,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1516,plain,
% 1.01/0.95 (((~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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1517,plain,
% 1.01/0.95 (((~![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))))),
% 1.01/0.95 inference(monotonicity,[status(thm)],[1516])).
% 1.01/0.95 tff(1518,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(transitivity,[status(thm)],[1517, 1515])).
% 1.01/0.95 tff(1519,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1520,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.01/0.95 tff(1521,plain,
% 1.01/0.95 (m_main_v_state1(s13, c_t1)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1520, 856, 1406, 1503])).
% 1.01/0.95 tff(1522,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1523,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1524,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.01/0.95 tff(1525,plain,
% 1.01/0.95 (~m_main_v_state2(s13, c_t2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1524, 77, 1453])).
% 1.01/0.95 tff(1526,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1527,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s13, c_t2) | (~node1(s13)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1528,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s13, c_t2) | (~node1(s13))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.01/0.95 tff(1529,plain,
% 1.01/0.95 (~node1(s13)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1528, 195, 1525])).
% 1.01/0.95 tff(1530,plain,
% 1.01/0.95 (succ(s13, s14) <=> succ(s13, s14)),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1531,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 1.01/0.95 tff(1532,plain,
% 1.01/0.95 (succ(s13, s14)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 1.01/0.95 tff(1533,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1534,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1535,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.01/0.95 tff(1536,plain,
% 1.01/0.95 (trans(s13, s14)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1535, 1532, 39])).
% 1.01/0.95 tff(1537,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1538,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s13, s14)) | node7(s13, s14))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1539,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s13, s14)) | node7(s13, s14)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 1.01/0.95 tff(1540,plain,
% 1.01/0.95 (node7(s13, s14)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1539, 206, 1536])).
% 1.01/0.95 tff(1541,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1542,plain,
% 1.01/0.95 (((~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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1543,plain,
% 1.01/0.95 (((~![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))))),
% 1.01/0.95 inference(monotonicity,[status(thm)],[1542])).
% 1.01/0.95 tff(1544,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(transitivity,[status(thm)],[1543, 1541])).
% 1.01/0.95 tff(1545,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1546,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.01/0.95 tff(1547,plain,
% 1.01/0.95 ((~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)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1546, 892, 1540])).
% 1.01/0.95 tff(1548,plain,
% 1.01/0.95 (m_main_v_state1(s14, c_c1)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1547, 1529, 1453, 1521, 1514, 1461])).
% 1.01/0.95 tff(1549,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1550,plain,
% 1.01/0.95 ((~![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)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1551,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 1.01/0.95 tff(1552,plain,
% 1.01/0.95 (~m_main_v_state1(s14, c_t1)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1551, 539, 1548])).
% 1.01/0.95 tff(1553,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1554,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s14, c_t1) | (~node5(s14)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1555,plain,
% 1.01/0.95 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s14, c_t1) | (~node5(s14))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.01/0.95 tff(1556,plain,
% 1.01/0.95 (~node5(s14)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1555, 550, 1552])).
% 1.01/0.95 tff(1557,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1558,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s13, s14)) | node14(s13, s14))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1559,plain,
% 1.01/0.95 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s13, s14)) | node14(s13, s14)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 1.01/0.95 tff(1560,plain,
% 1.01/0.95 (node14(s13, s14)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1559, 7, 1536])).
% 1.01/0.95 tff(1561,plain,
% 1.01/0.95 (((~![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))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(1562,plain,
% 1.01/0.95 ((~![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))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(1563,plain,
% 1.01/0.95 ((~![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)),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.01/0.95 tff(1564,plain,
% 1.01/0.95 ((~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_state2(s14, c_t2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1563, 922, 1560])).
% 1.01/0.95 tff(1565,plain,
% 1.01/0.95 (m_main_v_state2(s14, c_t2)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1564, 1521, 1453])).
% 1.01/0.95 tff(1566,plain,
% 1.01/0.95 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1567,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1568,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 1.01/0.96 tff(1569,plain,
% 1.01/0.96 (~m_main_v_state2(s14, c_n2)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1568, 77, 1565])).
% 1.01/0.96 tff(1570,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1571,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s14, c_n2) | (~node4(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1572,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s14, c_n2) | (~node4(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 1.01/0.96 tff(1573,plain,
% 1.01/0.96 (~node4(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1572, 388, 1569])).
% 1.01/0.96 tff(1574,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1575,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1576,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.01/0.96 tff(1577,plain,
% 1.01/0.96 (~m_main_v_state2(s14, c_c2)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1576, 260, 1565])).
% 1.01/0.96 tff(1578,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1579,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s14, c_c2) | (~node3(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1580,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s14, c_c2) | (~node3(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.01/0.96 tff(1581,plain,
% 1.01/0.96 (~node3(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1580, 399, 1577])).
% 1.01/0.96 tff(1582,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1583,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s14, c_n2) | (~node2(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1584,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s14, c_n2) | (~node2(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.01/0.96 tff(1585,plain,
% 1.01/0.96 (~node2(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1584, 410, 1569])).
% 1.01/0.96 tff(1586,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1587,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1588,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 1.01/0.96 tff(1589,plain,
% 1.01/0.96 (~m_main_v_state1(s14, c_n1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1588, 454, 1548])).
% 1.01/0.96 tff(1590,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1591,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s14, c_n1) | (~node1(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1592,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s14, c_n1) | (~node1(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.01/0.96 tff(1593,plain,
% 1.01/0.96 (~node1(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1592, 421, 1589])).
% 1.01/0.96 tff(1594,plain,
% 1.01/0.96 (succ(s14, s15) <=> succ(s14, s15)),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1595,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 1.01/0.96 tff(1596,plain,
% 1.01/0.96 (succ(s14, s15)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.01/0.96 tff(1597,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1598,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1599,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 1.01/0.96 tff(1600,plain,
% 1.01/0.96 (trans(s14, s15)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1599, 1596, 39])).
% 1.01/0.96 tff(1601,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1602,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s14, s15)) | node7(s14, s15))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1603,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s14, s15)) | node7(s14, s15)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.01/0.96 tff(1604,plain,
% 1.01/0.96 (node7(s14, s15)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1603, 206, 1600])).
% 1.01/0.96 tff(1605,plain,
% 1.01/0.96 (((~![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(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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1606,plain,
% 1.01/0.96 (((~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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1607,plain,
% 1.01/0.96 (((~![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(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))))),
% 1.01/0.96 inference(monotonicity,[status(thm)],[1606])).
% 1.01/0.96 tff(1608,plain,
% 1.01/0.96 (((~![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(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)))),
% 1.01/0.96 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.01/0.96 tff(1609,plain,
% 1.01/0.96 ((~![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(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15)) | m_main_v_state1(s15, c_n1))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1610,plain,
% 1.01/0.96 ((~![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(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14) | (~node7(s14, s15))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.01/0.96 tff(1611,plain,
% 1.01/0.96 (m_main_v_state1(s15, c_n1) | (~m_main_v_state1(s14, c_c1)) | node1(s14) | node2(s14) | node3(s14) | node4(s14) | node5(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1610, 584, 1604])).
% 1.01/0.96 tff(1612,plain,
% 1.01/0.96 (m_main_v_state1(s15, c_n1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1611, 1593, 1548, 1585, 1581, 1573, 1556])).
% 1.01/0.96 tff(1613,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1614,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s13, c_t2) | (~node15(s13)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1615,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s13, c_t2) | (~node15(s13))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.01/0.96 tff(1616,plain,
% 1.01/0.96 (~node15(s13)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1615, 103, 1525])).
% 1.01/0.96 tff(1617,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1618,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s13, s14)) | node18(s13, s14))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1619,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s13, s14)) | node18(s13, s14)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 1.01/0.96 tff(1620,plain,
% 1.01/0.96 (node18(s13, s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1619, 125, 1536])).
% 1.01/0.96 tff(1621,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1622,plain,
% 1.01/0.96 (((~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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1623,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(monotonicity,[status(thm)],[1622])).
% 1.01/0.96 tff(1624,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(transitivity,[status(thm)],[1623, 1621])).
% 1.01/0.96 tff(1625,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1626,plain,
% 1.01/0.96 ((~![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)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 1.01/0.96 tff(1627,plain,
% 1.01/0.96 (node15(s13) | (~m_main_v_state1(s13, c_t1)) | (~m_main_v_state2(s13, c_n2)) | m_main_v_turn(s14, c_1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1626, 992, 1620])).
% 1.01/0.96 tff(1628,plain,
% 1.01/0.96 (m_main_v_turn(s14, c_1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1627, 1616, 1453, 1521])).
% 1.01/0.96 tff(1629,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1630,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1631,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.01/0.96 tff(1632,plain,
% 1.01/0.96 (~m_main_v_turn(s14, c_2)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1631, 156, 1628])).
% 1.01/0.96 tff(1633,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1634,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s14, c_2) | (~node12(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1635,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s14, c_2) | (~node12(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 1.01/0.96 tff(1636,plain,
% 1.01/0.96 (~node12(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1635, 184, 1632])).
% 1.01/0.96 tff(1637,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1638,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s14, c_n2) | (~node8(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1639,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s14, c_n2) | (~node8(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.01/0.96 tff(1640,plain,
% 1.01/0.96 (~node8(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1639, 271, 1569])).
% 1.01/0.96 tff(1641,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1642,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s14, c_n2) | (~node9(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1643,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s14, c_n2) | (~node9(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.01/0.96 tff(1644,plain,
% 1.01/0.96 (~node9(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1643, 88, 1569])).
% 1.01/0.96 tff(1645,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1646,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s14, c_n2) | (~node10(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1647,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s14, c_n2) | (~node10(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.01/0.96 tff(1648,plain,
% 1.01/0.96 (~node10(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1647, 249, 1569])).
% 1.01/0.96 tff(1649,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1650,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s14, c_n1) | (~node11(s14)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1651,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s14, c_n1) | (~node11(s14))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.01/0.96 tff(1652,plain,
% 1.01/0.96 (~node11(s14)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1651, 238, 1589])).
% 1.01/0.96 tff(1653,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1654,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s14, s15)) | node14(s14, s15))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1655,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s14, s15)) | node14(s14, s15)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 1.01/0.96 tff(1656,plain,
% 1.01/0.96 (node14(s14, s15)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1655, 7, 1600])).
% 1.01/0.96 tff(1657,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1658,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1659,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.01/0.96 tff(1660,plain,
% 1.01/0.96 (m_main_v_state2(s14, c_c2) | node9(s14) | node8(s14) | node10(s14) | node11(s14) | node12(s14) | node13(s14, s15)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1659, 296, 1656])).
% 1.01/0.96 tff(1661,plain,
% 1.01/0.96 (node13(s14, s15)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1660, 1652, 1577, 1648, 1644, 1640, 1636])).
% 1.01/0.96 tff(1662,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1663,plain,
% 1.01/0.96 (((~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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1664,plain,
% 1.01/0.96 (((~![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))))),
% 1.01/0.96 inference(monotonicity,[status(thm)],[1663])).
% 1.01/0.96 tff(1665,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(transitivity,[status(thm)],[1664, 1662])).
% 1.01/0.96 tff(1666,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1667,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 1.01/0.96 tff(1668,plain,
% 1.01/0.96 (m_main_v_state2(s15, c_t2)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1667, 518, 1565, 1661])).
% 1.01/0.96 tff(1669,plain,
% 1.01/0.96 (succ(s15, s16) <=> succ(s15, s16)),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1670,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 1.01/0.96 tff(1671,plain,
% 1.01/0.96 (succ(s15, s16)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.01/0.96 tff(1672,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1673,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1674,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.01/0.96 tff(1675,plain,
% 1.01/0.96 (trans(s15, s16)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1674, 1671, 39])).
% 1.01/0.96 tff(1676,plain,
% 1.01/0.96 (((~![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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1677,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s15, s16)) | node7(s15, s16))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1678,plain,
% 1.01/0.96 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s15, s16)) | node7(s15, s16)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 1.01/0.96 tff(1679,plain,
% 1.01/0.96 (node7(s15, s16)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1678, 206, 1675])).
% 1.01/0.96 tff(1680,plain,
% 1.01/0.96 (((~![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(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))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1681,plain,
% 1.01/0.96 ((~![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(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1682,plain,
% 1.01/0.96 ((~![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(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node7(s15, s16)) | m_main_v_state1(s16, c_t1)),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 1.01/0.96 tff(1683,plain,
% 1.01/0.96 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_state1(s16, c_t1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1682, 651, 1679])).
% 1.01/0.96 tff(1684,plain,
% 1.01/0.96 (m_main_v_state1(s16, c_t1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1683, 1668, 1612])).
% 1.01/0.96 tff(1685,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1686,plain,
% 1.01/0.96 ((~![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)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1687,plain,
% 1.01/0.96 ((~![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))),
% 1.01/0.96 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 1.01/0.96 tff(1688,plain,
% 1.01/0.96 (~m_main_v_state1(s16, c_n1)),
% 1.01/0.96 inference(unit_resolution,[status(thm)],[1687, 17, 1684])).
% 1.01/0.96 tff(1689,plain,
% 1.01/0.96 (((~![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)))),
% 1.01/0.96 inference(rewrite,[status(thm)],[])).
% 1.01/0.96 tff(1690,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s16, c_n1) | (~node1(s16)))),
% 1.01/0.96 inference(quant_inst,[status(thm)],[])).
% 1.01/0.96 tff(1691,plain,
% 1.01/0.96 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s16, c_n1) | (~node1(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 1.01/0.97 tff(1692,plain,
% 1.01/0.97 (~node1(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1691, 421, 1688])).
% 1.01/0.97 tff(1693,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1694,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s15, s16)) | node18(s15, s16))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1695,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s15, s16)) | node18(s15, s16)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 1.01/0.97 tff(1696,plain,
% 1.01/0.97 (node18(s15, s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1695, 125, 1675])).
% 1.01/0.97 tff(1697,plain,
% 1.01/0.97 (((~![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(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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1698,plain,
% 1.01/0.97 ((~![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(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1699,plain,
% 1.01/0.97 ((~![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(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | (~node18(s15, s16)) | m_main_v_turn(s16, c_2)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 1.01/0.97 tff(1700,plain,
% 1.01/0.97 ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state2(s15, c_t2)) | m_main_v_turn(s16, c_2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1699, 760, 1696])).
% 1.01/0.97 tff(1701,plain,
% 1.01/0.97 (m_main_v_turn(s16, c_2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1700, 1668, 1612])).
% 1.01/0.97 tff(1702,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1703,plain,
% 1.01/0.97 ((~![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)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1704,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.01/0.97 tff(1705,plain,
% 1.01/0.97 (~m_main_v_turn(s16, c_1)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1704, 156, 1701])).
% 1.01/0.97 tff(1706,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1707,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s16, c_1) | (~node5(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1708,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s16, c_1) | (~node5(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 1.01/0.97 tff(1709,plain,
% 1.01/0.97 (~node5(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1708, 776, 1705])).
% 1.01/0.97 tff(1710,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1711,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s16, c_n1) | (~node2(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1712,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s16, c_n1) | (~node2(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 1.01/0.97 tff(1713,plain,
% 1.01/0.97 (~node2(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1712, 787, 1688])).
% 1.01/0.97 tff(1714,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1715,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s16, c_n1) | (~node3(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1716,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s16, c_n1) | (~node3(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.01/0.97 tff(1717,plain,
% 1.01/0.97 (~node3(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1716, 798, 1688])).
% 1.01/0.97 tff(1718,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1719,plain,
% 1.01/0.97 ((~![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)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1720,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 1.01/0.97 tff(1721,plain,
% 1.01/0.97 (~m_main_v_state1(s16, c_c1)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1720, 539, 1684])).
% 1.01/0.97 tff(1722,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1723,plain,
% 1.01/0.97 (((~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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1724,plain,
% 1.01/0.97 (((~![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))))),
% 1.01/0.97 inference(monotonicity,[status(thm)],[1723])).
% 1.01/0.97 tff(1725,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(transitivity,[status(thm)],[1724, 1722])).
% 1.01/0.97 tff(1726,plain,
% 1.01/0.97 ((~![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)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1727,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.01/0.97 tff(1728,plain,
% 1.01/0.97 (~m_main_v_state2(s15, c_n2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1727, 311, 1569, 1661])).
% 1.01/0.97 tff(1729,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1730,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s15, c_n2) | (~node9(s15)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1731,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s15, c_n2) | (~node9(s15))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.01/0.97 tff(1732,plain,
% 1.01/0.97 (~node9(s15)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1731, 88, 1728])).
% 1.01/0.97 tff(1733,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1734,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s15, c_n2) | (~node10(s15)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1735,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s15, c_n2) | (~node10(s15))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.01/0.97 tff(1736,plain,
% 1.01/0.97 (~node10(s15)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1735, 249, 1728])).
% 1.01/0.97 tff(1737,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1738,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s15, c_n2) | (~node8(s15)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1739,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s15, c_n2) | (~node8(s15))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.01/0.97 tff(1740,plain,
% 1.01/0.97 (~node8(s15)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1739, 271, 1728])).
% 1.01/0.97 tff(1741,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1742,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s15, s16)) | node14(s15, s16))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1743,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s15, s16)) | node14(s15, s16)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.01/0.97 tff(1744,plain,
% 1.01/0.97 (node14(s15, s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1743, 7, 1675])).
% 1.01/0.97 tff(1745,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1746,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1747,plain,
% 1.01/0.97 ((~![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)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.01/0.97 tff(1748,plain,
% 1.01/0.97 ((~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)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1747, 617, 1744])).
% 1.01/0.97 tff(1749,plain,
% 1.01/0.97 (m_main_v_state2(s16, c_c2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1748, 1740, 1612, 1668, 1736, 1732])).
% 1.01/0.97 tff(1750,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1751,plain,
% 1.01/0.97 ((~![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)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1752,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 1.01/0.97 tff(1753,plain,
% 1.01/0.97 (~m_main_v_state2(s16, c_n2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1752, 697, 1749])).
% 1.01/0.97 tff(1754,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1755,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s16, c_n2) | (~node4(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1756,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s16, c_n2) | (~node4(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 1.01/0.97 tff(1757,plain,
% 1.01/0.97 (~node4(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1756, 388, 1753])).
% 1.01/0.97 tff(1758,plain,
% 1.01/0.97 (succ(s16, s17) <=> succ(s16, s17)),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1759,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 1.01/0.97 tff(1760,plain,
% 1.01/0.97 (succ(s16, s17)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.01/0.97 tff(1761,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1762,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1763,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.01/0.97 tff(1764,plain,
% 1.01/0.97 (trans(s16, s17)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1763, 1760, 39])).
% 1.01/0.97 tff(1765,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1766,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s16, s17)) | node7(s16, s17))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1767,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s16, s17)) | node7(s16, s17)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.01/0.97 tff(1768,plain,
% 1.01/0.97 (node7(s16, s17)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1767, 206, 1764])).
% 1.01/0.97 tff(1769,plain,
% 1.01/0.97 (((~![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(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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1770,plain,
% 1.01/0.97 ((~![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(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1771,plain,
% 1.01/0.97 ((~![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(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17) | (~node7(s16, s17))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.01/0.97 tff(1772,plain,
% 1.01/0.97 (m_main_v_state1(s16, c_c1) | node1(s16) | node2(s16) | node3(s16) | node4(s16) | node5(s16) | node6(s16, s17)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1771, 820, 1768])).
% 1.01/0.97 tff(1773,plain,
% 1.01/0.97 (node6(s16, s17)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1772, 1757, 1721, 1717, 1713, 1709, 1692])).
% 1.01/0.97 tff(1774,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1775,plain,
% 1.01/0.97 (((~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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1776,plain,
% 1.01/0.97 (((~![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))))),
% 1.01/0.97 inference(monotonicity,[status(thm)],[1775])).
% 1.01/0.97 tff(1777,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.01/0.97 tff(1778,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1779,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.01/0.97 tff(1780,plain,
% 1.01/0.97 (m_main_v_state1(s17, c_t1)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1779, 856, 1684, 1773])).
% 1.01/0.97 tff(1781,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1782,plain,
% 1.01/0.97 ((~![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)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1783,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.01/0.97 tff(1784,plain,
% 1.01/0.97 (~m_main_v_state2(s16, c_t2)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1783, 260, 1749])).
% 1.01/0.97 tff(1785,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1786,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s16, c_t2) | (~node12(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1787,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s16, c_t2) | (~node12(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.01/0.97 tff(1788,plain,
% 1.01/0.97 (~node12(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1787, 633, 1784])).
% 1.01/0.97 tff(1789,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1790,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s16, c_n1) | (~node11(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1791,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s16, c_n1) | (~node11(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 1.01/0.97 tff(1792,plain,
% 1.01/0.97 (~node11(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1791, 238, 1688])).
% 1.01/0.97 tff(1793,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1794,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s16, c_c1) | (~node10(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1795,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s16, c_c1) | (~node10(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.01/0.97 tff(1796,plain,
% 1.01/0.97 (~node10(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1795, 675, 1721])).
% 1.01/0.97 tff(1797,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1798,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s16, c_n1) | (~node9(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1799,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s16, c_n1) | (~node9(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.01/0.97 tff(1800,plain,
% 1.01/0.97 (~node9(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1799, 686, 1688])).
% 1.01/0.97 tff(1801,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1802,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s16, c_n2) | (~node8(s16)))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1803,plain,
% 1.01/0.97 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s16, c_n2) | (~node8(s16))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 1.01/0.97 tff(1804,plain,
% 1.01/0.97 (~node8(s16)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1803, 271, 1753])).
% 1.01/0.97 tff(1805,plain,
% 1.01/0.97 (((~![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))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1806,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s16, s17)) | node14(s16, s17))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1807,plain,
% 1.01/0.97 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s16, s17)) | node14(s16, s17)),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.01/0.97 tff(1808,plain,
% 1.01/0.97 (node14(s16, s17)),
% 1.01/0.97 inference(unit_resolution,[status(thm)],[1807, 7, 1764])).
% 1.01/0.97 tff(1809,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1810,plain,
% 1.01/0.97 (((~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)))),
% 1.01/0.97 inference(rewrite,[status(thm)],[])).
% 1.01/0.97 tff(1811,plain,
% 1.01/0.97 (((~![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))))),
% 1.01/0.97 inference(monotonicity,[status(thm)],[1810])).
% 1.01/0.97 tff(1812,plain,
% 1.01/0.97 (((~![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)))),
% 1.01/0.97 inference(transitivity,[status(thm)],[1811, 1809])).
% 1.01/0.97 tff(1813,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(quant_inst,[status(thm)],[])).
% 1.01/0.97 tff(1814,plain,
% 1.01/0.97 ((~![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))),
% 1.01/0.97 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 1.01/0.98 tff(1815,plain,
% 1.01/0.98 (m_main_v_state2(s17, c_n2) | node9(s16) | node8(s16) | node10(s16) | node11(s16) | node12(s16) | (~m_main_v_state2(s16, c_c2))),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1814, 726, 1808])).
% 1.01/0.98 tff(1816,plain,
% 1.01/0.98 (m_main_v_state2(s17, c_n2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1815, 1804, 1749, 1800, 1796, 1792, 1788])).
% 1.01/0.98 tff(1817,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1818,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1819,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.01/0.98 tff(1820,plain,
% 1.01/0.98 (~m_main_v_state2(s17, c_t2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1819, 77, 1816])).
% 1.01/0.98 tff(1821,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1822,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s17, c_t2) | (~node15(s17)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1823,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s17, c_t2) | (~node15(s17))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 1.01/0.98 tff(1824,plain,
% 1.01/0.98 (~node15(s17)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1823, 103, 1820])).
% 1.01/0.98 tff(1825,plain,
% 1.01/0.98 (succ(s17, s18) <=> succ(s17, s18)),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1826,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 1.01/0.98 tff(1827,plain,
% 1.01/0.98 (succ(s17, s18)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 1.01/0.98 tff(1828,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1829,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1830,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.01/0.98 tff(1831,plain,
% 1.01/0.98 (trans(s17, s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1830, 1827, 39])).
% 1.01/0.98 tff(1832,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1833,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s17, s18)) | node18(s17, s18))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1834,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s17, s18)) | node18(s17, s18)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.01/0.98 tff(1835,plain,
% 1.01/0.98 (node18(s17, s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1834, 125, 1831])).
% 1.01/0.98 tff(1836,plain,
% 1.01/0.98 (((~![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(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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1837,plain,
% 1.01/0.98 (((~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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1838,plain,
% 1.01/0.98 (((~![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))) | ((~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)))),
% 1.01/0.98 inference(monotonicity,[status(thm)],[1837])).
% 1.01/0.98 tff(1839,plain,
% 1.01/0.98 (((~![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))) | ((~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))),
% 1.01/0.98 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.01/0.98 tff(1840,plain,
% 1.01/0.98 ((~![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))) | ((~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))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1841,plain,
% 1.01/0.98 ((~![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(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)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.01/0.98 tff(1842,plain,
% 1.01/0.98 (node15(s17) | (~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_turn(s18, c_1)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1841, 992, 1835])).
% 1.01/0.98 tff(1843,plain,
% 1.01/0.98 (m_main_v_turn(s18, c_1)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1842, 1824, 1816, 1780])).
% 1.01/0.98 tff(1844,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1845,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1846,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.01/0.98 tff(1847,plain,
% 1.01/0.98 (~m_main_v_turn(s18, c_2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1846, 156, 1843])).
% 1.01/0.98 tff(1848,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1849,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s18, c_2) | (~node12(s18)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1850,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s18, c_2) | (~node12(s18))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.01/0.98 tff(1851,plain,
% 1.01/0.98 (~node12(s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1850, 184, 1847])).
% 1.01/0.98 tff(1852,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1853,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s17, s18)) | node14(s17, s18))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1854,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s17, s18)) | node14(s17, s18)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.01/0.98 tff(1855,plain,
% 1.01/0.98 (node14(s17, s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1854, 7, 1831])).
% 1.01/0.98 tff(1856,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1857,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1858,plain,
% 1.01/0.98 ((~![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)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 1.01/0.98 tff(1859,plain,
% 1.01/0.98 ((~m_main_v_state1(s17, c_t1)) | (~m_main_v_state2(s17, c_n2)) | m_main_v_state2(s18, c_t2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1858, 922, 1855])).
% 1.01/0.98 tff(1860,plain,
% 1.01/0.98 (m_main_v_state2(s18, c_t2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1859, 1780, 1816])).
% 1.01/0.98 tff(1861,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1862,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1863,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.01/0.98 tff(1864,plain,
% 1.01/0.98 (~m_main_v_state2(s18, c_n2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1863, 77, 1860])).
% 1.01/0.98 tff(1865,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1866,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s18, c_n2) | (~node8(s18)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1867,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s18, c_n2) | (~node8(s18))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.01/0.98 tff(1868,plain,
% 1.01/0.98 (~node8(s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1867, 271, 1864])).
% 1.01/0.98 tff(1869,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1870,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s18, c_n2) | (~node9(s18)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1871,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s18, c_n2) | (~node9(s18))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 1.01/0.98 tff(1872,plain,
% 1.01/0.98 (~node9(s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1871, 88, 1864])).
% 1.01/0.98 tff(1873,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1874,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s18, c_n2) | (~node10(s18)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1875,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s18, c_n2) | (~node10(s18))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 1.01/0.98 tff(1876,plain,
% 1.01/0.98 (~node10(s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1875, 249, 1864])).
% 1.01/0.98 tff(1877,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1878,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1879,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.01/0.98 tff(1880,plain,
% 1.01/0.98 (~m_main_v_state2(s18, c_c2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1879, 260, 1860])).
% 1.01/0.98 tff(1881,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1882,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1883,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 1.01/0.98 tff(1884,plain,
% 1.01/0.98 (~m_main_v_state2(s17, c_c2)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1883, 697, 1816])).
% 1.01/0.98 tff(1885,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1886,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s17, c_c2) | (~node3(s17)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1887,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s17, c_c2) | (~node3(s17))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.01/0.98 tff(1888,plain,
% 1.01/0.98 (~node3(s17)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1887, 399, 1884])).
% 1.01/0.98 tff(1889,plain,
% 1.01/0.98 (((~![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(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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1890,plain,
% 1.01/0.98 (((~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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1891,plain,
% 1.01/0.98 (((~![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))))),
% 1.01/0.98 inference(monotonicity,[status(thm)],[1890])).
% 1.01/0.98 tff(1892,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(transitivity,[status(thm)],[1891, 1889])).
% 1.01/0.98 tff(1893,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1894,plain,
% 1.01/0.98 ((~![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(s16, c_n1) | (~m_main_v_state1(s17, c_n1)) | (~node6(s16, s17))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.01/0.98 tff(1895,plain,
% 1.01/0.98 (~m_main_v_state1(s17, c_n1)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1894, 835, 1688, 1773])).
% 1.01/0.98 tff(1896,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1897,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s17, c_n1) | (~node2(s17)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1898,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s17, c_n1) | (~node2(s17))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.01/0.98 tff(1899,plain,
% 1.01/0.98 (~node2(s17)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1898, 787, 1895])).
% 1.01/0.98 tff(1900,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1901,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s17, c_t2) | (~node1(s17)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1902,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s17, c_t2) | (~node1(s17))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 1.01/0.98 tff(1903,plain,
% 1.01/0.98 (~node1(s17)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1902, 195, 1820])).
% 1.01/0.98 tff(1904,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1905,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s17, s18)) | node7(s17, s18))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1906,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s17, s18)) | node7(s17, s18)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.01/0.98 tff(1907,plain,
% 1.01/0.98 (node7(s17, s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1906, 206, 1831])).
% 1.01/0.98 tff(1908,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1909,plain,
% 1.01/0.98 (((~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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1910,plain,
% 1.01/0.98 (((~![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))))),
% 1.01/0.98 inference(monotonicity,[status(thm)],[1909])).
% 1.01/0.98 tff(1911,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(transitivity,[status(thm)],[1910, 1908])).
% 1.01/0.98 tff(1912,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1913,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 1.01/0.98 tff(1914,plain,
% 1.01/0.98 ((~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)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1913, 892, 1907])).
% 1.01/0.98 tff(1915,plain,
% 1.01/0.98 (m_main_v_state1(s18, c_c1)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1914, 1903, 1816, 1780, 1899, 1888])).
% 1.01/0.98 tff(1916,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1917,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1918,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 1.01/0.98 tff(1919,plain,
% 1.01/0.98 (~m_main_v_state1(s18, c_n1)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1918, 454, 1915])).
% 1.01/0.98 tff(1920,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1921,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s18, c_n1) | (~node11(s18)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1922,plain,
% 1.01/0.98 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s18, c_n1) | (~node11(s18))),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.01/0.98 tff(1923,plain,
% 1.01/0.98 (~node11(s18)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1922, 238, 1919])).
% 1.01/0.98 tff(1924,plain,
% 1.01/0.98 (succ(s18, s19) <=> succ(s18, s19)),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1925,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 1.01/0.98 tff(1926,plain,
% 1.01/0.98 (succ(s18, s19)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.01/0.98 tff(1927,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1928,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1929,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 1.01/0.98 tff(1930,plain,
% 1.01/0.98 (trans(s18, s19)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1929, 1926, 39])).
% 1.01/0.98 tff(1931,plain,
% 1.01/0.98 (((~![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))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1932,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s18, s19)) | node14(s18, s19))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1933,plain,
% 1.01/0.98 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s18, s19)) | node14(s18, s19)),
% 1.01/0.98 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.01/0.98 tff(1934,plain,
% 1.01/0.98 (node14(s18, s19)),
% 1.01/0.98 inference(unit_resolution,[status(thm)],[1933, 7, 1930])).
% 1.01/0.98 tff(1935,plain,
% 1.01/0.98 (((~![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)))),
% 1.01/0.98 inference(rewrite,[status(thm)],[])).
% 1.01/0.98 tff(1936,plain,
% 1.01/0.98 ((~![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)))),
% 1.01/0.98 inference(quant_inst,[status(thm)],[])).
% 1.01/0.98 tff(1937,plain,
% 1.01/0.98 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.01/0.99 tff(1938,plain,
% 1.01/0.99 (m_main_v_state2(s18, c_c2) | node9(s18) | node8(s18) | node10(s18) | node11(s18) | node12(s18) | node13(s18, s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1937, 296, 1934])).
% 1.01/0.99 tff(1939,plain,
% 1.01/0.99 (node13(s18, s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1938, 1923, 1880, 1876, 1872, 1868, 1851])).
% 1.01/0.99 tff(1940,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1941,plain,
% 1.01/0.99 (((~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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1942,plain,
% 1.01/0.99 (((~![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))))),
% 1.01/0.99 inference(monotonicity,[status(thm)],[1941])).
% 1.01/0.99 tff(1943,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(transitivity,[status(thm)],[1942, 1940])).
% 1.01/0.99 tff(1944,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1945,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.01/0.99 tff(1946,plain,
% 1.01/0.99 (~m_main_v_state2(s19, c_n2)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1945, 311, 1864, 1939])).
% 1.01/0.99 tff(1947,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1948,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s19, c_n2) | (~node9(s19)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1949,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s19, c_n2) | (~node9(s19))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 1.01/0.99 tff(1950,plain,
% 1.01/0.99 (~node9(s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1949, 88, 1946])).
% 1.01/0.99 tff(1951,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1952,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s19, c_n2) | (~node10(s19)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1953,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s19, c_n2) | (~node10(s19))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.01/0.99 tff(1954,plain,
% 1.01/0.99 (~node10(s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1953, 249, 1946])).
% 1.01/0.99 tff(1955,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1956,plain,
% 1.01/0.99 (((~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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1957,plain,
% 1.01/0.99 (((~![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))))),
% 1.01/0.99 inference(monotonicity,[status(thm)],[1956])).
% 1.01/0.99 tff(1958,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(transitivity,[status(thm)],[1957, 1955])).
% 1.01/0.99 tff(1959,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1960,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 1.01/0.99 tff(1961,plain,
% 1.01/0.99 (m_main_v_state2(s19, c_t2)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1960, 518, 1860, 1939])).
% 1.01/0.99 tff(1962,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1963,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1964,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.01/0.99 tff(1965,plain,
% 1.01/0.99 (~m_main_v_state1(s18, c_t1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1964, 539, 1915])).
% 1.01/0.99 tff(1966,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1967,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s18, c_t1) | (~node5(s18)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1968,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s18, c_t1) | (~node5(s18))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.01/0.99 tff(1969,plain,
% 1.01/0.99 (~node5(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1968, 550, 1965])).
% 1.01/0.99 tff(1970,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1971,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s18, c_n2) | (~node4(s18)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1972,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s18, c_n2) | (~node4(s18))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1971, 1970])).
% 1.01/0.99 tff(1973,plain,
% 1.01/0.99 (~node4(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1972, 388, 1864])).
% 1.01/0.99 tff(1974,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1975,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s18, c_c2) | (~node3(s18)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1976,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s18, c_c2) | (~node3(s18))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 1.01/0.99 tff(1977,plain,
% 1.01/0.99 (~node3(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1976, 399, 1880])).
% 1.01/0.99 tff(1978,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1979,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s18, c_n2) | (~node2(s18)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1980,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s18, c_n2) | (~node2(s18))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.01/0.99 tff(1981,plain,
% 1.01/0.99 (~node2(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1980, 410, 1864])).
% 1.01/0.99 tff(1982,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1983,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s18, c_n1) | (~node1(s18)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1984,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s18, c_n1) | (~node1(s18))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.01/0.99 tff(1985,plain,
% 1.01/0.99 (~node1(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1984, 421, 1919])).
% 1.01/0.99 tff(1986,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1987,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s18, s19)) | node7(s18, s19))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1988,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s18, s19)) | node7(s18, s19)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 1.01/0.99 tff(1989,plain,
% 1.01/0.99 (node7(s18, s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1988, 206, 1930])).
% 1.01/0.99 tff(1990,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1991,plain,
% 1.01/0.99 (((~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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1992,plain,
% 1.01/0.99 (((~![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))))),
% 1.01/0.99 inference(monotonicity,[status(thm)],[1991])).
% 1.01/0.99 tff(1993,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(transitivity,[status(thm)],[1992, 1990])).
% 1.01/0.99 tff(1994,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(1995,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 1.01/0.99 tff(1996,plain,
% 1.01/0.99 (m_main_v_state1(s19, c_n1) | (~m_main_v_state1(s18, c_c1)) | node1(s18) | node2(s18) | node3(s18) | node4(s18) | node5(s18)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1995, 584, 1989])).
% 1.01/0.99 tff(1997,plain,
% 1.01/0.99 (m_main_v_state1(s19, c_n1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[1996, 1985, 1915, 1981, 1977, 1973, 1969])).
% 1.01/0.99 tff(1998,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(1999,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s19, c_n2) | (~node8(s19)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2000,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s19, c_n2) | (~node8(s19))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.01/0.99 tff(2001,plain,
% 1.01/0.99 (~node8(s19)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2000, 271, 1946])).
% 1.01/0.99 tff(2002,plain,
% 1.01/0.99 (succ(s19, s20) <=> succ(s19, s20)),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2003,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 1.01/0.99 tff(2004,plain,
% 1.01/0.99 (succ(s19, s20)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.01/0.99 tff(2005,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2006,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2007,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 1.01/0.99 tff(2008,plain,
% 1.01/0.99 (trans(s19, s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2007, 2004, 39])).
% 1.01/0.99 tff(2009,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2010,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s19, s20)) | node14(s19, s20))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2011,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s19, s20)) | node14(s19, s20)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 1.01/0.99 tff(2012,plain,
% 1.01/0.99 (node14(s19, s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2011, 7, 2008])).
% 1.01/0.99 tff(2013,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2014,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2015,plain,
% 1.01/0.99 ((~![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)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.01/0.99 tff(2016,plain,
% 1.01/0.99 ((~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)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2015, 617, 2012])).
% 1.01/0.99 tff(2017,plain,
% 1.01/0.99 (m_main_v_state2(s20, c_c2)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2016, 2001, 1997, 1961, 1954, 1950])).
% 1.01/0.99 tff(2018,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2019,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2020,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 1.01/0.99 tff(2021,plain,
% 1.01/0.99 (~m_main_v_state2(s20, c_t2)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2020, 260, 2017])).
% 1.01/0.99 tff(2022,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2023,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s20, c_t2) | (~node12(s20)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2024,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s20, c_t2) | (~node12(s20))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 1.01/0.99 tff(2025,plain,
% 1.01/0.99 (~node12(s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2024, 633, 2021])).
% 1.01/0.99 tff(2026,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2027,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s19, s20)) | node7(s19, s20))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2028,plain,
% 1.01/0.99 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s19, s20)) | node7(s19, s20)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.01/0.99 tff(2029,plain,
% 1.01/0.99 (node7(s19, s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2028, 206, 2008])).
% 1.01/0.99 tff(2030,plain,
% 1.01/0.99 (((~![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))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2031,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2032,plain,
% 1.01/0.99 ((~![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)),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.01/0.99 tff(2033,plain,
% 1.01/0.99 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_state1(s20, c_t1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2032, 651, 2029])).
% 1.01/0.99 tff(2034,plain,
% 1.01/0.99 (m_main_v_state1(s20, c_t1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2033, 1961, 1997])).
% 1.01/0.99 tff(2035,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2036,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2037,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 1.01/0.99 tff(2038,plain,
% 1.01/0.99 (~m_main_v_state1(s20, c_n1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2037, 17, 2034])).
% 1.01/0.99 tff(2039,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2040,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s20, c_n1) | (~node11(s20)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2041,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s20, c_n1) | (~node11(s20))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 1.01/0.99 tff(2042,plain,
% 1.01/0.99 (~node11(s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2041, 238, 2038])).
% 1.01/0.99 tff(2043,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2044,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2045,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.01/0.99 tff(2046,plain,
% 1.01/0.99 (~m_main_v_state1(s20, c_c1)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2045, 539, 2034])).
% 1.01/0.99 tff(2047,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2048,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s20, c_c1) | (~node10(s20)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2049,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s20, c_c1) | (~node10(s20))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2048, 2047])).
% 1.01/0.99 tff(2050,plain,
% 1.01/0.99 (~node10(s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2049, 675, 2046])).
% 1.01/0.99 tff(2051,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2052,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s20, c_n1) | (~node9(s20)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2053,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s20, c_n1) | (~node9(s20))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 1.01/0.99 tff(2054,plain,
% 1.01/0.99 (~node9(s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2053, 686, 2038])).
% 1.01/0.99 tff(2055,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2056,plain,
% 1.01/0.99 ((~![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)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2057,plain,
% 1.01/0.99 ((~![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))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.01/0.99 tff(2058,plain,
% 1.01/0.99 (~m_main_v_state2(s20, c_n2)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2057, 697, 2017])).
% 1.01/0.99 tff(2059,plain,
% 1.01/0.99 (((~![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)))),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/0.99 tff(2060,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s20, c_n2) | (~node8(s20)))),
% 1.01/0.99 inference(quant_inst,[status(thm)],[])).
% 1.01/0.99 tff(2061,plain,
% 1.01/0.99 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s20, c_n2) | (~node8(s20))),
% 1.01/0.99 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 1.01/0.99 tff(2062,plain,
% 1.01/0.99 (~node8(s20)),
% 1.01/0.99 inference(unit_resolution,[status(thm)],[2061, 271, 2058])).
% 1.01/0.99 tff(2063,plain,
% 1.01/0.99 (succ(s20, s21) <=> succ(s20, s21)),
% 1.01/0.99 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2064,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 1.01/1.00 tff(2065,plain,
% 1.01/1.00 (succ(s20, s21)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.01/1.00 tff(2066,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2067,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2068,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 1.01/1.00 tff(2069,plain,
% 1.01/1.00 (trans(s20, s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2068, 2065, 39])).
% 1.01/1.00 tff(2070,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2071,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s20, s21)) | node14(s20, s21))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2072,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s20, s21)) | node14(s20, s21)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 1.01/1.00 tff(2073,plain,
% 1.01/1.00 (node14(s20, s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2072, 7, 2069])).
% 1.01/1.00 tff(2074,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2075,plain,
% 1.01/1.00 (((~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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2076,plain,
% 1.01/1.00 (((~![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))))),
% 1.01/1.00 inference(monotonicity,[status(thm)],[2075])).
% 1.01/1.00 tff(2077,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(transitivity,[status(thm)],[2076, 2074])).
% 1.01/1.00 tff(2078,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2079,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.01/1.00 tff(2080,plain,
% 1.01/1.00 (m_main_v_state2(s21, c_n2) | node9(s20) | node8(s20) | node10(s20) | node11(s20) | node12(s20) | (~m_main_v_state2(s20, c_c2))),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2079, 726, 2073])).
% 1.01/1.00 tff(2081,plain,
% 1.01/1.00 (m_main_v_state2(s21, c_n2)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2080, 2062, 2017, 2054, 2050, 2042, 2025])).
% 1.01/1.00 tff(2082,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2083,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2084,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.01/1.00 tff(2085,plain,
% 1.01/1.00 (~m_main_v_state2(s21, c_c2)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2084, 697, 2081])).
% 1.01/1.00 tff(2086,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2087,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s21, c_c2) | (~node3(s21)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2088,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s21, c_c2) | (~node3(s21))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 1.01/1.00 tff(2089,plain,
% 1.01/1.00 (~node3(s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2088, 399, 2085])).
% 1.01/1.00 tff(2090,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2091,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s20, c_n1) | (~node1(s20)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2092,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s20, c_n1) | (~node1(s20))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 1.01/1.00 tff(2093,plain,
% 1.01/1.00 (~node1(s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2092, 421, 2038])).
% 1.01/1.00 tff(2094,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2095,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s19, s20)) | node18(s19, s20))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2096,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s19, s20)) | node18(s19, s20)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.01/1.00 tff(2097,plain,
% 1.01/1.00 (node18(s19, s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2096, 125, 2008])).
% 1.01/1.00 tff(2098,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2099,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2100,plain,
% 1.01/1.00 ((~![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)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 1.01/1.00 tff(2101,plain,
% 1.01/1.00 ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state2(s19, c_t2)) | m_main_v_turn(s20, c_2)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2100, 760, 2097])).
% 1.01/1.00 tff(2102,plain,
% 1.01/1.00 (m_main_v_turn(s20, c_2)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2101, 1961, 1997])).
% 1.01/1.00 tff(2103,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2104,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2105,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 1.01/1.00 tff(2106,plain,
% 1.01/1.00 (~m_main_v_turn(s20, c_1)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2105, 156, 2102])).
% 1.01/1.00 tff(2107,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2108,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s20, c_1) | (~node5(s20)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2109,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s20, c_1) | (~node5(s20))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.01/1.00 tff(2110,plain,
% 1.01/1.00 (~node5(s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2109, 776, 2106])).
% 1.01/1.00 tff(2111,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2112,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s20, c_n1) | (~node2(s20)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2113,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s20, c_n1) | (~node2(s20))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.01/1.00 tff(2114,plain,
% 1.01/1.00 (~node2(s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2113, 787, 2038])).
% 1.01/1.00 tff(2115,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2116,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s20, c_n1) | (~node3(s20)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2117,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s20, c_n1) | (~node3(s20))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.01/1.00 tff(2118,plain,
% 1.01/1.00 (~node3(s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2117, 798, 2038])).
% 1.01/1.00 tff(2119,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2120,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s20, c_n2) | (~node4(s20)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2121,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s20, c_n2) | (~node4(s20))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 1.01/1.00 tff(2122,plain,
% 1.01/1.00 (~node4(s20)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2121, 388, 2058])).
% 1.01/1.00 tff(2123,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2124,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s20, s21)) | node7(s20, s21))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2125,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s20, s21)) | node7(s20, s21)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.01/1.00 tff(2126,plain,
% 1.01/1.00 (node7(s20, s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2125, 206, 2069])).
% 1.01/1.00 tff(2127,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2128,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2129,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.01/1.00 tff(2130,plain,
% 1.01/1.00 (m_main_v_state1(s20, c_c1) | node1(s20) | node2(s20) | node3(s20) | node4(s20) | node5(s20) | node6(s20, s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2129, 820, 2126])).
% 1.01/1.00 tff(2131,plain,
% 1.01/1.00 (node6(s20, s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2130, 2122, 2046, 2118, 2114, 2110, 2093])).
% 1.01/1.00 tff(2132,plain,
% 1.01/1.00 (((~![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)))) <=> ((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2133,plain,
% 1.01/1.00 (((~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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2134,plain,
% 1.01/1.00 (((~![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))))),
% 1.01/1.00 inference(monotonicity,[status(thm)],[2133])).
% 1.01/1.00 tff(2135,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(transitivity,[status(thm)],[2134, 2132])).
% 1.01/1.00 tff(2136,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2137,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 1.01/1.00 tff(2138,plain,
% 1.01/1.00 (~m_main_v_state1(s21, c_n1)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2137, 835, 2038, 2131])).
% 1.01/1.00 tff(2139,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2140,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s21, c_n1) | (~node2(s21)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2141,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s21, c_n1) | (~node2(s21))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.01/1.00 tff(2142,plain,
% 1.01/1.00 (~node2(s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2141, 787, 2138])).
% 1.01/1.00 tff(2143,plain,
% 1.01/1.00 (((~![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_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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2144,plain,
% 1.01/1.00 (((~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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2145,plain,
% 1.01/1.00 (((~![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_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))))),
% 1.01/1.00 inference(monotonicity,[status(thm)],[2144])).
% 1.01/1.00 tff(2146,plain,
% 1.01/1.00 (((~![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_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)))),
% 1.01/1.00 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.01/1.00 tff(2147,plain,
% 1.01/1.00 ((~![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_t1)) | m_main_v_state1(s21, c_t1))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2148,plain,
% 1.01/1.00 ((~![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_t1)) | m_main_v_state1(s21, c_t1) | (~node6(s20, s21))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.01/1.00 tff(2149,plain,
% 1.01/1.00 (m_main_v_state1(s21, c_t1)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2148, 856, 2034, 2131])).
% 1.01/1.00 tff(2150,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2151,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2152,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.01/1.00 tff(2153,plain,
% 1.01/1.00 (~m_main_v_state2(s21, c_t2)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2152, 77, 2081])).
% 1.01/1.00 tff(2154,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2155,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s21, c_t2) | (~node1(s21)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2156,plain,
% 1.01/1.00 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s21, c_t2) | (~node1(s21))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.01/1.00 tff(2157,plain,
% 1.01/1.00 (~node1(s21)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2156, 195, 2153])).
% 1.01/1.00 tff(2158,plain,
% 1.01/1.00 (succ(s21, s22) <=> succ(s21, s22)),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2159,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 1.01/1.00 tff(2160,plain,
% 1.01/1.00 (succ(s21, s22)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.01/1.00 tff(2161,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2162,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2163,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.01/1.00 tff(2164,plain,
% 1.01/1.00 (trans(s21, s22)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2163, 2160, 39])).
% 1.01/1.00 tff(2165,plain,
% 1.01/1.00 (((~![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))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2166,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s21, s22)) | node7(s21, s22))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2167,plain,
% 1.01/1.00 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s21, s22)) | node7(s21, s22)),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 1.01/1.00 tff(2168,plain,
% 1.01/1.00 (node7(s21, s22)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2167, 206, 2164])).
% 1.01/1.00 tff(2169,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2170,plain,
% 1.01/1.00 (((~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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2171,plain,
% 1.01/1.00 (((~![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))))),
% 1.01/1.00 inference(monotonicity,[status(thm)],[2170])).
% 1.01/1.00 tff(2172,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.01/1.00 tff(2173,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2174,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.01/1.00 tff(2175,plain,
% 1.01/1.00 ((~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)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2174, 892, 2168])).
% 1.01/1.00 tff(2176,plain,
% 1.01/1.00 (m_main_v_state1(s22, c_c1)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2175, 2157, 2081, 2149, 2142, 2089])).
% 1.01/1.00 tff(2177,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.00 inference(rewrite,[status(thm)],[])).
% 1.01/1.00 tff(2178,plain,
% 1.01/1.00 ((~![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)))),
% 1.01/1.00 inference(quant_inst,[status(thm)],[])).
% 1.01/1.00 tff(2179,plain,
% 1.01/1.00 ((~![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))),
% 1.01/1.00 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 1.01/1.00 tff(2180,plain,
% 1.01/1.00 (~m_main_v_state1(s22, c_t1)),
% 1.01/1.00 inference(unit_resolution,[status(thm)],[2179, 539, 2176])).
% 1.01/1.00 tff(2181,plain,
% 1.01/1.00 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2182,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s22, c_t1) | (~node5(s22)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2183,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s22, c_t1) | (~node5(s22))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.01/1.01 tff(2184,plain,
% 1.01/1.01 (~node5(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2183, 550, 2180])).
% 1.01/1.01 tff(2185,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2186,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s21, s22)) | node14(s21, s22))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2187,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s21, s22)) | node14(s21, s22)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 1.01/1.01 tff(2188,plain,
% 1.01/1.01 (node14(s21, s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2187, 7, 2164])).
% 1.01/1.01 tff(2189,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2190,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2191,plain,
% 1.01/1.01 ((~![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)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.01/1.01 tff(2192,plain,
% 1.01/1.01 ((~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_state2(s22, c_t2)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2191, 922, 2188])).
% 1.01/1.01 tff(2193,plain,
% 1.01/1.01 (m_main_v_state2(s22, c_t2)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2192, 2149, 2081])).
% 1.01/1.01 tff(2194,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2195,plain,
% 1.01/1.01 ((~![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)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2196,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.01/1.01 tff(2197,plain,
% 1.01/1.01 (~m_main_v_state2(s22, c_n2)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2196, 77, 2193])).
% 1.01/1.01 tff(2198,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2199,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s22, c_n2) | (~node4(s22)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2200,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s22, c_n2) | (~node4(s22))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 1.01/1.01 tff(2201,plain,
% 1.01/1.01 (~node4(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2200, 388, 2197])).
% 1.01/1.01 tff(2202,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2203,plain,
% 1.01/1.01 ((~![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)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2204,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 1.01/1.01 tff(2205,plain,
% 1.01/1.01 (~m_main_v_state2(s22, c_c2)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2204, 260, 2193])).
% 1.01/1.01 tff(2206,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2207,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s22, c_c2) | (~node3(s22)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2208,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s22, c_c2) | (~node3(s22))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.01/1.01 tff(2209,plain,
% 1.01/1.01 (~node3(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2208, 399, 2205])).
% 1.01/1.01 tff(2210,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2211,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s22, c_n2) | (~node2(s22)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2212,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s22, c_n2) | (~node2(s22))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.01/1.01 tff(2213,plain,
% 1.01/1.01 (~node2(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2212, 410, 2197])).
% 1.01/1.01 tff(2214,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2215,plain,
% 1.01/1.01 ((~![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)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2216,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.01/1.01 tff(2217,plain,
% 1.01/1.01 (~m_main_v_state1(s22, c_n1)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2216, 454, 2176])).
% 1.01/1.01 tff(2218,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2219,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s22, c_n1) | (~node1(s22)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2220,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s22, c_n1) | (~node1(s22))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.01/1.01 tff(2221,plain,
% 1.01/1.01 (~node1(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2220, 421, 2217])).
% 1.01/1.01 tff(2222,plain,
% 1.01/1.01 (succ(s22, s23) <=> succ(s22, s23)),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2223,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 1.01/1.01 tff(2224,plain,
% 1.01/1.01 (succ(s22, s23)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 1.01/1.01 tff(2225,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2226,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2227,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.01/1.01 tff(2228,plain,
% 1.01/1.01 (trans(s22, s23)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2227, 2224, 39])).
% 1.01/1.01 tff(2229,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2230,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s22, s23)) | node7(s22, s23))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2231,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s22, s23)) | node7(s22, s23)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.01/1.01 tff(2232,plain,
% 1.01/1.01 (node7(s22, s23)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2231, 206, 2228])).
% 1.01/1.01 tff(2233,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2234,plain,
% 1.01/1.01 (((~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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2235,plain,
% 1.01/1.01 (((~![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))))),
% 1.01/1.01 inference(monotonicity,[status(thm)],[2234])).
% 1.01/1.01 tff(2236,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(transitivity,[status(thm)],[2235, 2233])).
% 1.01/1.01 tff(2237,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2238,plain,
% 1.01/1.01 ((~![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))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 1.01/1.01 tff(2239,plain,
% 1.01/1.01 (m_main_v_state1(s23, c_n1) | (~m_main_v_state1(s22, c_c1)) | node1(s22) | node2(s22) | node3(s22) | node4(s22) | node5(s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2238, 584, 2232])).
% 1.01/1.01 tff(2240,plain,
% 1.01/1.01 (m_main_v_state1(s23, c_n1)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2239, 2221, 2176, 2213, 2209, 2201, 2184])).
% 1.01/1.01 tff(2241,plain,
% 1.01/1.01 (((~![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)))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2242,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s21, c_t2) | (~node15(s21)))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2243,plain,
% 1.01/1.01 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s21, c_t2) | (~node15(s21))),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 1.01/1.01 tff(2244,plain,
% 1.01/1.01 (~node15(s21)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2243, 103, 2153])).
% 1.01/1.01 tff(2245,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2246,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s21, s22)) | node18(s21, s22))),
% 1.01/1.01 inference(quant_inst,[status(thm)],[])).
% 1.01/1.01 tff(2247,plain,
% 1.01/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s21, s22)) | node18(s21, s22)),
% 1.01/1.01 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 1.01/1.01 tff(2248,plain,
% 1.01/1.01 (node18(s21, s22)),
% 1.01/1.01 inference(unit_resolution,[status(thm)],[2247, 125, 2164])).
% 1.01/1.01 tff(2249,plain,
% 1.01/1.01 (((~![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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2250,plain,
% 1.01/1.01 (((~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))),
% 1.01/1.01 inference(rewrite,[status(thm)],[])).
% 1.01/1.01 tff(2251,plain,
% 1.01/1.01 (((~![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)))),
% 1.10/1.01 inference(monotonicity,[status(thm)],[2250])).
% 1.10/1.01 tff(2252,plain,
% 1.10/1.01 (((~![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))),
% 1.10/1.01 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.10/1.01 tff(2253,plain,
% 1.10/1.01 ((~![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))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2254,plain,
% 1.10/1.01 ((~![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)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.10/1.01 tff(2255,plain,
% 1.10/1.01 (node15(s21) | (~m_main_v_state1(s21, c_t1)) | (~m_main_v_state2(s21, c_n2)) | m_main_v_turn(s22, c_1)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2254, 992, 2248])).
% 1.10/1.01 tff(2256,plain,
% 1.10/1.01 (m_main_v_turn(s22, c_1)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2255, 2244, 2081, 2149])).
% 1.10/1.01 tff(2257,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2258,plain,
% 1.10/1.01 ((~![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)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2259,plain,
% 1.10/1.01 ((~![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))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.10/1.01 tff(2260,plain,
% 1.10/1.01 (~m_main_v_turn(s22, c_2)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2259, 156, 2256])).
% 1.10/1.01 tff(2261,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2262,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s22, c_2) | (~node12(s22)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2263,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s22, c_2) | (~node12(s22))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 1.10/1.01 tff(2264,plain,
% 1.10/1.01 (~node12(s22)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2263, 184, 2260])).
% 1.10/1.01 tff(2265,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2266,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s22, c_n2) | (~node8(s22)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2267,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s22, c_n2) | (~node8(s22))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 1.10/1.01 tff(2268,plain,
% 1.10/1.01 (~node8(s22)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2267, 271, 2197])).
% 1.10/1.01 tff(2269,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2270,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s22, c_n2) | (~node9(s22)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2271,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s22, c_n2) | (~node9(s22))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 1.10/1.01 tff(2272,plain,
% 1.10/1.01 (~node9(s22)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2271, 88, 2197])).
% 1.10/1.01 tff(2273,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2274,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s22, c_n2) | (~node10(s22)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2275,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s22, c_n2) | (~node10(s22))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.10/1.01 tff(2276,plain,
% 1.10/1.01 (~node10(s22)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2275, 249, 2197])).
% 1.10/1.01 tff(2277,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2278,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s22, c_n1) | (~node11(s22)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2279,plain,
% 1.10/1.01 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s22, c_n1) | (~node11(s22))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.10/1.01 tff(2280,plain,
% 1.10/1.01 (~node11(s22)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2279, 238, 2217])).
% 1.10/1.01 tff(2281,plain,
% 1.10/1.01 (((~![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))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2282,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s22, s23)) | node14(s22, s23))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2283,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s22, s23)) | node14(s22, s23)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.10/1.01 tff(2284,plain,
% 1.10/1.01 (node14(s22, s23)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2283, 7, 2228])).
% 1.10/1.01 tff(2285,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2286,plain,
% 1.10/1.01 ((~![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)))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2287,plain,
% 1.10/1.01 ((~![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))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 1.10/1.01 tff(2288,plain,
% 1.10/1.01 (m_main_v_state2(s22, c_c2) | node9(s22) | node8(s22) | node10(s22) | node11(s22) | node12(s22) | node13(s22, s23)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2287, 296, 2284])).
% 1.10/1.01 tff(2289,plain,
% 1.10/1.01 (node13(s22, s23)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2288, 2280, 2205, 2276, 2272, 2268, 2264])).
% 1.10/1.01 tff(2290,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2291,plain,
% 1.10/1.01 (((~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)))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2292,plain,
% 1.10/1.01 (((~![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))))),
% 1.10/1.01 inference(monotonicity,[status(thm)],[2291])).
% 1.10/1.01 tff(2293,plain,
% 1.10/1.01 (((~![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)))),
% 1.10/1.01 inference(transitivity,[status(thm)],[2292, 2290])).
% 1.10/1.01 tff(2294,plain,
% 1.10/1.01 ((~![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))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2295,plain,
% 1.10/1.01 ((~![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))),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 1.10/1.01 tff(2296,plain,
% 1.10/1.01 (m_main_v_state2(s23, c_t2)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2295, 518, 2193, 2289])).
% 1.10/1.01 tff(2297,plain,
% 1.10/1.01 (succ(s23, s24) <=> succ(s23, s24)),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2298,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 1.10/1.01 tff(2299,plain,
% 1.10/1.01 (succ(s23, s24)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.10/1.01 tff(2300,plain,
% 1.10/1.01 (((~![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))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2301,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2302,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.10/1.01 tff(2303,plain,
% 1.10/1.01 (trans(s23, s24)),
% 1.10/1.01 inference(unit_resolution,[status(thm)],[2302, 2299, 39])).
% 1.10/1.01 tff(2304,plain,
% 1.10/1.01 (((~![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))),
% 1.10/1.01 inference(rewrite,[status(thm)],[])).
% 1.10/1.01 tff(2305,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s23, s24)) | node7(s23, s24))),
% 1.10/1.01 inference(quant_inst,[status(thm)],[])).
% 1.10/1.01 tff(2306,plain,
% 1.10/1.01 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s23, s24)) | node7(s23, s24)),
% 1.10/1.01 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 1.10/1.02 tff(2307,plain,
% 1.10/1.02 (node7(s23, s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2306, 206, 2303])).
% 1.10/1.02 tff(2308,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2309,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2310,plain,
% 1.10/1.02 ((~![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)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 1.10/1.02 tff(2311,plain,
% 1.10/1.02 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_state1(s24, c_t1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2310, 651, 2307])).
% 1.10/1.02 tff(2312,plain,
% 1.10/1.02 (m_main_v_state1(s24, c_t1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2311, 2296, 2240])).
% 1.10/1.02 tff(2313,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2314,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2315,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 1.10/1.02 tff(2316,plain,
% 1.10/1.02 (~m_main_v_state1(s24, c_n1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2315, 17, 2312])).
% 1.10/1.02 tff(2317,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2318,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s24, c_n1) | (~node1(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2319,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s24, c_n1) | (~node1(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 1.10/1.02 tff(2320,plain,
% 1.10/1.02 (~node1(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2319, 421, 2316])).
% 1.10/1.02 tff(2321,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2322,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s23, s24)) | node18(s23, s24))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2323,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s23, s24)) | node18(s23, s24)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 1.10/1.02 tff(2324,plain,
% 1.10/1.02 (node18(s23, s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2323, 125, 2303])).
% 1.10/1.02 tff(2325,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2326,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2327,plain,
% 1.10/1.02 ((~![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)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.10/1.02 tff(2328,plain,
% 1.10/1.02 ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state2(s23, c_t2)) | m_main_v_turn(s24, c_2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2327, 760, 2324])).
% 1.10/1.02 tff(2329,plain,
% 1.10/1.02 (m_main_v_turn(s24, c_2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2328, 2296, 2240])).
% 1.10/1.02 tff(2330,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2331,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2332,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.10/1.02 tff(2333,plain,
% 1.10/1.02 (~m_main_v_turn(s24, c_1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2332, 156, 2329])).
% 1.10/1.02 tff(2334,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2335,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s24, c_1) | (~node5(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2336,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s24, c_1) | (~node5(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.10/1.02 tff(2337,plain,
% 1.10/1.02 (~node5(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2336, 776, 2333])).
% 1.10/1.02 tff(2338,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2339,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s24, c_n1) | (~node2(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2340,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s24, c_n1) | (~node2(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.10/1.02 tff(2341,plain,
% 1.10/1.02 (~node2(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2340, 787, 2316])).
% 1.10/1.02 tff(2342,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2343,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s24, c_n1) | (~node3(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2344,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s24, c_n1) | (~node3(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.10/1.02 tff(2345,plain,
% 1.10/1.02 (~node3(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2344, 798, 2316])).
% 1.10/1.02 tff(2346,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2347,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2348,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 1.10/1.02 tff(2349,plain,
% 1.10/1.02 (~m_main_v_state1(s24, c_c1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2348, 539, 2312])).
% 1.10/1.02 tff(2350,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2351,plain,
% 1.10/1.02 (((~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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2352,plain,
% 1.10/1.02 (((~![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))))),
% 1.10/1.02 inference(monotonicity,[status(thm)],[2351])).
% 1.10/1.02 tff(2353,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.10/1.02 tff(2354,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2355,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.10/1.02 tff(2356,plain,
% 1.10/1.02 (~m_main_v_state2(s23, c_n2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2355, 311, 2197, 2289])).
% 1.10/1.02 tff(2357,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2358,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s23, c_n2) | (~node9(s23)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2359,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s23, c_n2) | (~node9(s23))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 1.10/1.02 tff(2360,plain,
% 1.10/1.02 (~node9(s23)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2359, 88, 2356])).
% 1.10/1.02 tff(2361,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2362,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s23, c_n2) | (~node10(s23)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2363,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s23, c_n2) | (~node10(s23))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 1.10/1.02 tff(2364,plain,
% 1.10/1.02 (~node10(s23)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2363, 249, 2356])).
% 1.10/1.02 tff(2365,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2366,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s23, c_n2) | (~node8(s23)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2367,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s23, c_n2) | (~node8(s23))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.10/1.02 tff(2368,plain,
% 1.10/1.02 (~node8(s23)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2367, 271, 2356])).
% 1.10/1.02 tff(2369,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2370,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s23, s24)) | node14(s23, s24))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2371,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s23, s24)) | node14(s23, s24)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 1.10/1.02 tff(2372,plain,
% 1.10/1.02 (node14(s23, s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2371, 7, 2303])).
% 1.10/1.02 tff(2373,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2374,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2375,plain,
% 1.10/1.02 ((~![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)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.10/1.02 tff(2376,plain,
% 1.10/1.02 ((~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)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2375, 617, 2372])).
% 1.10/1.02 tff(2377,plain,
% 1.10/1.02 (m_main_v_state2(s24, c_c2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2376, 2368, 2240, 2296, 2364, 2360])).
% 1.10/1.02 tff(2378,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2379,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2380,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2379, 2378])).
% 1.10/1.02 tff(2381,plain,
% 1.10/1.02 (~m_main_v_state2(s24, c_n2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2380, 697, 2377])).
% 1.10/1.02 tff(2382,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2383,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s24, c_n2) | (~node4(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2384,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s24, c_n2) | (~node4(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.10/1.02 tff(2385,plain,
% 1.10/1.02 (~node4(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2384, 388, 2381])).
% 1.10/1.02 tff(2386,plain,
% 1.10/1.02 (succ(s24, s25) <=> succ(s24, s25)),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2387,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 1.10/1.02 tff(2388,plain,
% 1.10/1.02 (succ(s24, s25)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 1.10/1.02 tff(2389,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2390,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2391,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.10/1.02 tff(2392,plain,
% 1.10/1.02 (trans(s24, s25)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2391, 2388, 39])).
% 1.10/1.02 tff(2393,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2394,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s24, s25)) | node7(s24, s25))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2395,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s24, s25)) | node7(s24, s25)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 1.10/1.02 tff(2396,plain,
% 1.10/1.02 (node7(s24, s25)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2395, 206, 2392])).
% 1.10/1.02 tff(2397,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2398,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2399,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.10/1.02 tff(2400,plain,
% 1.10/1.02 (m_main_v_state1(s24, c_c1) | node1(s24) | node2(s24) | node3(s24) | node4(s24) | node5(s24) | node6(s24, s25)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2399, 820, 2396])).
% 1.10/1.02 tff(2401,plain,
% 1.10/1.02 (node6(s24, s25)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2400, 2385, 2349, 2345, 2341, 2337, 2320])).
% 1.10/1.02 tff(2402,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2403,plain,
% 1.10/1.02 (((~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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2404,plain,
% 1.10/1.02 (((~![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))))),
% 1.10/1.02 inference(monotonicity,[status(thm)],[2403])).
% 1.10/1.02 tff(2405,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.10/1.02 tff(2406,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2407,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.10/1.02 tff(2408,plain,
% 1.10/1.02 (m_main_v_state1(s25, c_t1)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2407, 856, 2312, 2401])).
% 1.10/1.02 tff(2409,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2410,plain,
% 1.10/1.02 ((~![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)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2411,plain,
% 1.10/1.02 ((~![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))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.10/1.02 tff(2412,plain,
% 1.10/1.02 (~m_main_v_state2(s24, c_t2)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2411, 260, 2377])).
% 1.10/1.02 tff(2413,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2414,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s24, c_t2) | (~node12(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2415,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s24, c_t2) | (~node12(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.10/1.02 tff(2416,plain,
% 1.10/1.02 (~node12(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2415, 633, 2412])).
% 1.10/1.02 tff(2417,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2418,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s24, c_n1) | (~node11(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2419,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s24, c_n1) | (~node11(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2418, 2417])).
% 1.10/1.02 tff(2420,plain,
% 1.10/1.02 (~node11(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2419, 238, 2316])).
% 1.10/1.02 tff(2421,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2422,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s24, c_c1) | (~node10(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2423,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s24, c_c1) | (~node10(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.10/1.02 tff(2424,plain,
% 1.10/1.02 (~node10(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2423, 675, 2349])).
% 1.10/1.02 tff(2425,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2426,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s24, c_n1) | (~node9(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2427,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s24, c_n1) | (~node9(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 1.10/1.02 tff(2428,plain,
% 1.10/1.02 (~node9(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2427, 686, 2316])).
% 1.10/1.02 tff(2429,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2430,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s24, c_n2) | (~node8(s24)))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2431,plain,
% 1.10/1.02 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s24, c_n2) | (~node8(s24))),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 1.10/1.02 tff(2432,plain,
% 1.10/1.02 (~node8(s24)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2431, 271, 2381])).
% 1.10/1.02 tff(2433,plain,
% 1.10/1.02 (((~![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))),
% 1.10/1.02 inference(rewrite,[status(thm)],[])).
% 1.10/1.02 tff(2434,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s24, s25)) | node14(s24, s25))),
% 1.10/1.02 inference(quant_inst,[status(thm)],[])).
% 1.10/1.02 tff(2435,plain,
% 1.10/1.02 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s24, s25)) | node14(s24, s25)),
% 1.10/1.02 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 1.10/1.02 tff(2436,plain,
% 1.10/1.02 (node14(s24, s25)),
% 1.10/1.02 inference(unit_resolution,[status(thm)],[2435, 7, 2392])).
% 1.10/1.02 tff(2437,plain,
% 1.10/1.02 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2438,plain,
% 1.10/1.03 (((~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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2439,plain,
% 1.10/1.03 (((~![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))))),
% 1.10/1.03 inference(monotonicity,[status(thm)],[2438])).
% 1.10/1.03 tff(2440,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(transitivity,[status(thm)],[2439, 2437])).
% 1.10/1.03 tff(2441,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2442,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 1.10/1.03 tff(2443,plain,
% 1.10/1.03 (m_main_v_state2(s25, c_n2) | node9(s24) | node8(s24) | node10(s24) | node11(s24) | node12(s24) | (~m_main_v_state2(s24, c_c2))),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2442, 726, 2436])).
% 1.10/1.03 tff(2444,plain,
% 1.10/1.03 (m_main_v_state2(s25, c_n2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2443, 2432, 2377, 2428, 2424, 2420, 2416])).
% 1.10/1.03 tff(2445,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2446,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2447,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.10/1.03 tff(2448,plain,
% 1.10/1.03 (~m_main_v_state2(s25, c_t2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2447, 77, 2444])).
% 1.10/1.03 tff(2449,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2450,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s25, c_t2) | (~node15(s25)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2451,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s25, c_t2) | (~node15(s25))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.10/1.03 tff(2452,plain,
% 1.10/1.03 (~node15(s25)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2451, 103, 2448])).
% 1.10/1.03 tff(2453,plain,
% 1.10/1.03 (succ(s25, s26) <=> succ(s25, s26)),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2454,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 1.10/1.03 tff(2455,plain,
% 1.10/1.03 (succ(s25, s26)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.10/1.03 tff(2456,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2457,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2458,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 1.10/1.03 tff(2459,plain,
% 1.10/1.03 (trans(s25, s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2458, 2455, 39])).
% 1.10/1.03 tff(2460,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2461,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s25, s26)) | node18(s25, s26))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2462,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s25, s26)) | node18(s25, s26)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.10/1.03 tff(2463,plain,
% 1.10/1.03 (node18(s25, s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2462, 125, 2459])).
% 1.10/1.03 tff(2464,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2465,plain,
% 1.10/1.03 (((~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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2466,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(monotonicity,[status(thm)],[2465])).
% 1.10/1.03 tff(2467,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.10/1.03 tff(2468,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2469,plain,
% 1.10/1.03 ((~![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)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.10/1.03 tff(2470,plain,
% 1.10/1.03 (node15(s25) | (~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_turn(s26, c_1)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2469, 992, 2463])).
% 1.10/1.03 tff(2471,plain,
% 1.10/1.03 (m_main_v_turn(s26, c_1)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2470, 2452, 2444, 2408])).
% 1.10/1.03 tff(2472,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2473,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2474,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.10/1.03 tff(2475,plain,
% 1.10/1.03 (~m_main_v_turn(s26, c_2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2474, 156, 2471])).
% 1.10/1.03 tff(2476,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2477,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s26, c_2) | (~node12(s26)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2478,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s26, c_2) | (~node12(s26))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.10/1.03 tff(2479,plain,
% 1.10/1.03 (~node12(s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2478, 184, 2475])).
% 1.10/1.03 tff(2480,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2481,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s25, s26)) | node14(s25, s26))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2482,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s25, s26)) | node14(s25, s26)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.10/1.03 tff(2483,plain,
% 1.10/1.03 (node14(s25, s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2482, 7, 2459])).
% 1.10/1.03 tff(2484,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2485,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2486,plain,
% 1.10/1.03 ((~![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)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 1.10/1.03 tff(2487,plain,
% 1.10/1.03 ((~m_main_v_state1(s25, c_t1)) | (~m_main_v_state2(s25, c_n2)) | m_main_v_state2(s26, c_t2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2486, 922, 2483])).
% 1.10/1.03 tff(2488,plain,
% 1.10/1.03 (m_main_v_state2(s26, c_t2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2487, 2408, 2444])).
% 1.10/1.03 tff(2489,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2490,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2491,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 1.10/1.03 tff(2492,plain,
% 1.10/1.03 (~m_main_v_state2(s26, c_n2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2491, 77, 2488])).
% 1.10/1.03 tff(2493,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2494,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s26, c_n2) | (~node8(s26)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2495,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s26, c_n2) | (~node8(s26))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 1.10/1.03 tff(2496,plain,
% 1.10/1.03 (~node8(s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2495, 271, 2492])).
% 1.10/1.03 tff(2497,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2498,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s26, c_n2) | (~node9(s26)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2499,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s26, c_n2) | (~node9(s26))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 1.10/1.03 tff(2500,plain,
% 1.10/1.03 (~node9(s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2499, 88, 2492])).
% 1.10/1.03 tff(2501,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2502,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s26, c_n2) | (~node10(s26)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2503,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s26, c_n2) | (~node10(s26))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.10/1.03 tff(2504,plain,
% 1.10/1.03 (~node10(s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2503, 249, 2492])).
% 1.10/1.03 tff(2505,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2506,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2507,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 1.10/1.03 tff(2508,plain,
% 1.10/1.03 (~m_main_v_state2(s26, c_c2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2507, 260, 2488])).
% 1.10/1.03 tff(2509,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2510,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2511,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.10/1.03 tff(2512,plain,
% 1.10/1.03 (~m_main_v_state2(s25, c_c2)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2511, 697, 2444])).
% 1.10/1.03 tff(2513,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2514,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s25, c_c2) | (~node3(s25)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2515,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s25, c_c2) | (~node3(s25))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 1.10/1.03 tff(2516,plain,
% 1.10/1.03 (~node3(s25)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2515, 399, 2512])).
% 1.10/1.03 tff(2517,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2518,plain,
% 1.10/1.03 (((~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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2519,plain,
% 1.10/1.03 (((~![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))))),
% 1.10/1.03 inference(monotonicity,[status(thm)],[2518])).
% 1.10/1.03 tff(2520,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(transitivity,[status(thm)],[2519, 2517])).
% 1.10/1.03 tff(2521,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2522,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 1.10/1.03 tff(2523,plain,
% 1.10/1.03 (~m_main_v_state1(s25, c_n1)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2522, 835, 2316, 2401])).
% 1.10/1.03 tff(2524,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2525,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s25, c_n1) | (~node2(s25)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2526,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s25, c_n1) | (~node2(s25))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2525, 2524])).
% 1.10/1.03 tff(2527,plain,
% 1.10/1.03 (~node2(s25)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2526, 787, 2523])).
% 1.10/1.03 tff(2528,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2529,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s25, c_t2) | (~node1(s25)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2530,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s25, c_t2) | (~node1(s25))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 1.10/1.03 tff(2531,plain,
% 1.10/1.03 (~node1(s25)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2530, 195, 2448])).
% 1.10/1.03 tff(2532,plain,
% 1.10/1.03 (((~![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))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2533,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s25, s26)) | node7(s25, s26))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2534,plain,
% 1.10/1.03 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s25, s26)) | node7(s25, s26)),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.10/1.03 tff(2535,plain,
% 1.10/1.03 (node7(s25, s26)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2534, 206, 2459])).
% 1.10/1.03 tff(2536,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2537,plain,
% 1.10/1.03 (((~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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2538,plain,
% 1.10/1.03 (((~![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))))),
% 1.10/1.03 inference(monotonicity,[status(thm)],[2537])).
% 1.10/1.03 tff(2539,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.10/1.03 tff(2540,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2541,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.10/1.03 tff(2542,plain,
% 1.10/1.03 ((~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)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2541, 892, 2535])).
% 1.10/1.03 tff(2543,plain,
% 1.10/1.03 (m_main_v_state1(s26, c_c1)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2542, 2531, 2444, 2408, 2527, 2516])).
% 1.10/1.03 tff(2544,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2545,plain,
% 1.10/1.03 ((~![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)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2546,plain,
% 1.10/1.03 ((~![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))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 1.10/1.03 tff(2547,plain,
% 1.10/1.03 (~m_main_v_state1(s26, c_n1)),
% 1.10/1.03 inference(unit_resolution,[status(thm)],[2546, 454, 2543])).
% 1.10/1.03 tff(2548,plain,
% 1.10/1.03 (((~![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)))),
% 1.10/1.03 inference(rewrite,[status(thm)],[])).
% 1.10/1.03 tff(2549,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s26, c_n1) | (~node11(s26)))),
% 1.10/1.03 inference(quant_inst,[status(thm)],[])).
% 1.10/1.03 tff(2550,plain,
% 1.10/1.03 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s26, c_n1) | (~node11(s26))),
% 1.10/1.03 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 1.10/1.03 tff(2551,plain,
% 1.10/1.03 (~node11(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2550, 238, 2547])).
% 1.10/1.04 tff(2552,plain,
% 1.10/1.04 (succ(s26, s27) <=> succ(s26, s27)),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2553,axiom,(succ(s26, s27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound27')).
% 1.10/1.04 tff(2554,plain,
% 1.10/1.04 (succ(s26, s27)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 1.10/1.04 tff(2555,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2556,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2557,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.10/1.04 tff(2558,plain,
% 1.10/1.04 (trans(s26, s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2557, 2554, 39])).
% 1.10/1.04 tff(2559,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2560,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s26, s27)) | node14(s26, s27))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2561,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s26, s27)) | node14(s26, s27)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.10/1.04 tff(2562,plain,
% 1.10/1.04 (node14(s26, s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2561, 7, 2558])).
% 1.10/1.04 tff(2563,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2564,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2565,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 1.10/1.04 tff(2566,plain,
% 1.10/1.04 (m_main_v_state2(s26, c_c2) | node9(s26) | node8(s26) | node10(s26) | node11(s26) | node12(s26) | node13(s26, s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2565, 296, 2562])).
% 1.10/1.04 tff(2567,plain,
% 1.10/1.04 (node13(s26, s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2566, 2551, 2508, 2504, 2500, 2496, 2479])).
% 1.10/1.04 tff(2568,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2569,plain,
% 1.10/1.04 (((~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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2570,plain,
% 1.10/1.04 (((~![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))))),
% 1.10/1.04 inference(monotonicity,[status(thm)],[2569])).
% 1.10/1.04 tff(2571,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(transitivity,[status(thm)],[2570, 2568])).
% 1.10/1.04 tff(2572,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2573,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 1.10/1.04 tff(2574,plain,
% 1.10/1.04 (~m_main_v_state2(s27, c_n2)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2573, 311, 2492, 2567])).
% 1.10/1.04 tff(2575,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2576,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s27, c_n2) | (~node9(s27)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2577,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s27, c_n2) | (~node9(s27))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2576, 2575])).
% 1.10/1.04 tff(2578,plain,
% 1.10/1.04 (~node9(s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2577, 88, 2574])).
% 1.10/1.04 tff(2579,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2580,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s27, c_n2) | (~node10(s27)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2581,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s27, c_n2) | (~node10(s27))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.10/1.04 tff(2582,plain,
% 1.10/1.04 (~node10(s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2581, 249, 2574])).
% 1.10/1.04 tff(2583,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2584,plain,
% 1.10/1.04 (((~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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2585,plain,
% 1.10/1.04 (((~![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))))),
% 1.10/1.04 inference(monotonicity,[status(thm)],[2584])).
% 1.10/1.04 tff(2586,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.10/1.04 tff(2587,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2588,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.10/1.04 tff(2589,plain,
% 1.10/1.04 (m_main_v_state2(s27, c_t2)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2588, 518, 2488, 2567])).
% 1.10/1.04 tff(2590,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2591,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2592,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 1.10/1.04 tff(2593,plain,
% 1.10/1.04 (~m_main_v_state1(s26, c_t1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2592, 539, 2543])).
% 1.10/1.04 tff(2594,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2595,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s26, c_t1) | (~node5(s26)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2596,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s26, c_t1) | (~node5(s26))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.10/1.04 tff(2597,plain,
% 1.10/1.04 (~node5(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2596, 550, 2593])).
% 1.10/1.04 tff(2598,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2599,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s26, c_n2) | (~node4(s26)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2600,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s26, c_n2) | (~node4(s26))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2599, 2598])).
% 1.10/1.04 tff(2601,plain,
% 1.10/1.04 (~node4(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2600, 388, 2492])).
% 1.10/1.04 tff(2602,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2603,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s26, c_c2) | (~node3(s26)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2604,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s26, c_c2) | (~node3(s26))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.10/1.04 tff(2605,plain,
% 1.10/1.04 (~node3(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2604, 399, 2508])).
% 1.10/1.04 tff(2606,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2607,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s26, c_n2) | (~node2(s26)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2608,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s26, c_n2) | (~node2(s26))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.10/1.04 tff(2609,plain,
% 1.10/1.04 (~node2(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2608, 410, 2492])).
% 1.10/1.04 tff(2610,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2611,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s26, c_n1) | (~node1(s26)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2612,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s26, c_n1) | (~node1(s26))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 1.10/1.04 tff(2613,plain,
% 1.10/1.04 (~node1(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2612, 421, 2547])).
% 1.10/1.04 tff(2614,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2615,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s26, s27)) | node7(s26, s27))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2616,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s26, s27)) | node7(s26, s27)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.10/1.04 tff(2617,plain,
% 1.10/1.04 (node7(s26, s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2616, 206, 2558])).
% 1.10/1.04 tff(2618,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2619,plain,
% 1.10/1.04 (((~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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2620,plain,
% 1.10/1.04 (((~![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))))),
% 1.10/1.04 inference(monotonicity,[status(thm)],[2619])).
% 1.10/1.04 tff(2621,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(transitivity,[status(thm)],[2620, 2618])).
% 1.10/1.04 tff(2622,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2623,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.10/1.04 tff(2624,plain,
% 1.10/1.04 (m_main_v_state1(s27, c_n1) | (~m_main_v_state1(s26, c_c1)) | node1(s26) | node2(s26) | node3(s26) | node4(s26) | node5(s26)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2623, 584, 2617])).
% 1.10/1.04 tff(2625,plain,
% 1.10/1.04 (m_main_v_state1(s27, c_n1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2624, 2613, 2543, 2609, 2605, 2601, 2597])).
% 1.10/1.04 tff(2626,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2627,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s27, c_n2) | (~node8(s27)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2628,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s27, c_n2) | (~node8(s27))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 1.10/1.04 tff(2629,plain,
% 1.10/1.04 (~node8(s27)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2628, 271, 2574])).
% 1.10/1.04 tff(2630,plain,
% 1.10/1.04 (succ(s27, s28) <=> succ(s27, s28)),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2631,axiom,(succ(s27, s28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound28')).
% 1.10/1.04 tff(2632,plain,
% 1.10/1.04 (succ(s27, s28)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.10/1.04 tff(2633,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2634,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2635,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.10/1.04 tff(2636,plain,
% 1.10/1.04 (trans(s27, s28)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2635, 2632, 39])).
% 1.10/1.04 tff(2637,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2638,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s27, s28)) | node14(s27, s28))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2639,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s27, s28)) | node14(s27, s28)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 1.10/1.04 tff(2640,plain,
% 1.10/1.04 (node14(s27, s28)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2639, 7, 2636])).
% 1.10/1.04 tff(2641,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2642,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2643,plain,
% 1.10/1.04 ((~![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)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 1.10/1.04 tff(2644,plain,
% 1.10/1.04 ((~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)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2643, 617, 2640])).
% 1.10/1.04 tff(2645,plain,
% 1.10/1.04 (m_main_v_state2(s28, c_c2)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2644, 2629, 2625, 2589, 2582, 2578])).
% 1.10/1.04 tff(2646,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2647,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2648,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2647, 2646])).
% 1.10/1.04 tff(2649,plain,
% 1.10/1.04 (~m_main_v_state2(s28, c_t2)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2648, 260, 2645])).
% 1.10/1.04 tff(2650,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2651,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s28, c_t2) | (~node12(s28)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2652,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s28, c_t2) | (~node12(s28))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2651, 2650])).
% 1.10/1.04 tff(2653,plain,
% 1.10/1.04 (~node12(s28)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2652, 633, 2649])).
% 1.10/1.04 tff(2654,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2655,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s27, s28)) | node7(s27, s28))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2656,plain,
% 1.10/1.04 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s27, s28)) | node7(s27, s28)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.10/1.04 tff(2657,plain,
% 1.10/1.04 (node7(s27, s28)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2656, 206, 2636])).
% 1.10/1.04 tff(2658,plain,
% 1.10/1.04 (((~![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))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2659,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2660,plain,
% 1.10/1.04 ((~![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)),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 1.10/1.04 tff(2661,plain,
% 1.10/1.04 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_state1(s28, c_t1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2660, 651, 2657])).
% 1.10/1.04 tff(2662,plain,
% 1.10/1.04 (m_main_v_state1(s28, c_t1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2661, 2589, 2625])).
% 1.10/1.04 tff(2663,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2664,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2665,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.10/1.04 tff(2666,plain,
% 1.10/1.04 (~m_main_v_state1(s28, c_n1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2665, 17, 2662])).
% 1.10/1.04 tff(2667,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2668,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s28, c_n1) | (~node11(s28)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2669,plain,
% 1.10/1.04 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s28, c_n1) | (~node11(s28))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.10/1.04 tff(2670,plain,
% 1.10/1.04 (~node11(s28)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2669, 238, 2666])).
% 1.10/1.04 tff(2671,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.04 inference(rewrite,[status(thm)],[])).
% 1.10/1.04 tff(2672,plain,
% 1.10/1.04 ((~![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)))),
% 1.10/1.04 inference(quant_inst,[status(thm)],[])).
% 1.10/1.04 tff(2673,plain,
% 1.10/1.04 ((~![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))),
% 1.10/1.04 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.10/1.04 tff(2674,plain,
% 1.10/1.04 (~m_main_v_state1(s28, c_c1)),
% 1.10/1.04 inference(unit_resolution,[status(thm)],[2673, 539, 2662])).
% 1.10/1.04 tff(2675,plain,
% 1.10/1.04 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2676,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s28, c_c1) | (~node10(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2677,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s28, c_c1) | (~node10(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2676, 2675])).
% 1.10/1.05 tff(2678,plain,
% 1.10/1.05 (~node10(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2677, 675, 2674])).
% 1.10/1.05 tff(2679,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2680,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s28, c_n1) | (~node9(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2681,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s28, c_n1) | (~node9(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 1.10/1.05 tff(2682,plain,
% 1.10/1.05 (~node9(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2681, 686, 2666])).
% 1.10/1.05 tff(2683,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2684,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2685,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.10/1.05 tff(2686,plain,
% 1.10/1.05 (~m_main_v_state2(s28, c_n2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2685, 697, 2645])).
% 1.10/1.05 tff(2687,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2688,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s28, c_n2) | (~node8(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2689,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s28, c_n2) | (~node8(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 1.10/1.05 tff(2690,plain,
% 1.10/1.05 (~node8(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2689, 271, 2686])).
% 1.10/1.05 tff(2691,plain,
% 1.10/1.05 (succ(s28, s29) <=> succ(s28, s29)),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2692,axiom,(succ(s28, s29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound29')).
% 1.10/1.05 tff(2693,plain,
% 1.10/1.05 (succ(s28, s29)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 1.10/1.05 tff(2694,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2695,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2696,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 1.10/1.05 tff(2697,plain,
% 1.10/1.05 (trans(s28, s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2696, 2693, 39])).
% 1.10/1.05 tff(2698,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2699,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s28, s29)) | node14(s28, s29))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2700,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s28, s29)) | node14(s28, s29)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2699, 2698])).
% 1.10/1.05 tff(2701,plain,
% 1.10/1.05 (node14(s28, s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2700, 7, 2697])).
% 1.10/1.05 tff(2702,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2703,plain,
% 1.10/1.05 (((~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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2704,plain,
% 1.10/1.05 (((~![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))))),
% 1.10/1.05 inference(monotonicity,[status(thm)],[2703])).
% 1.10/1.05 tff(2705,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(transitivity,[status(thm)],[2704, 2702])).
% 1.10/1.05 tff(2706,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2707,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 1.10/1.05 tff(2708,plain,
% 1.10/1.05 (m_main_v_state2(s29, c_n2) | node9(s28) | node8(s28) | node10(s28) | node11(s28) | node12(s28) | (~m_main_v_state2(s28, c_c2))),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2707, 726, 2701])).
% 1.10/1.05 tff(2709,plain,
% 1.10/1.05 (m_main_v_state2(s29, c_n2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2708, 2690, 2645, 2682, 2678, 2670, 2653])).
% 1.10/1.05 tff(2710,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2711,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2712,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.10/1.05 tff(2713,plain,
% 1.10/1.05 (~m_main_v_state2(s29, c_c2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2712, 697, 2709])).
% 1.10/1.05 tff(2714,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2715,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s29, c_c2) | (~node3(s29)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2716,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s29, c_c2) | (~node3(s29))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.10/1.05 tff(2717,plain,
% 1.10/1.05 (~node3(s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2716, 399, 2713])).
% 1.10/1.05 tff(2718,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2719,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s28, c_n1) | (~node1(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2720,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s28, c_n1) | (~node1(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 1.10/1.05 tff(2721,plain,
% 1.10/1.05 (~node1(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2720, 421, 2666])).
% 1.10/1.05 tff(2722,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2723,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s27, s28)) | node18(s27, s28))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2724,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s27, s28)) | node18(s27, s28)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.10/1.05 tff(2725,plain,
% 1.10/1.05 (node18(s27, s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2724, 125, 2636])).
% 1.10/1.05 tff(2726,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2727,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2728,plain,
% 1.10/1.05 ((~![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)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 1.10/1.05 tff(2729,plain,
% 1.10/1.05 ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state2(s27, c_t2)) | m_main_v_turn(s28, c_2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2728, 760, 2725])).
% 1.10/1.05 tff(2730,plain,
% 1.10/1.05 (m_main_v_turn(s28, c_2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2729, 2589, 2625])).
% 1.10/1.05 tff(2731,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2732,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2733,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.10/1.05 tff(2734,plain,
% 1.10/1.05 (~m_main_v_turn(s28, c_1)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2733, 156, 2730])).
% 1.10/1.05 tff(2735,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2736,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s28, c_1) | (~node5(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2737,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s28, c_1) | (~node5(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 1.10/1.05 tff(2738,plain,
% 1.10/1.05 (~node5(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2737, 776, 2734])).
% 1.10/1.05 tff(2739,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2740,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s28, c_n1) | (~node2(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2741,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s28, c_n1) | (~node2(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 1.10/1.05 tff(2742,plain,
% 1.10/1.05 (~node2(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2741, 787, 2666])).
% 1.10/1.05 tff(2743,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2744,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s28, c_n1) | (~node3(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2745,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s28, c_n1) | (~node3(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 1.10/1.05 tff(2746,plain,
% 1.10/1.05 (~node3(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2745, 798, 2666])).
% 1.10/1.05 tff(2747,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2748,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s28, c_n2) | (~node4(s28)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2749,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s28, c_n2) | (~node4(s28))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 1.10/1.05 tff(2750,plain,
% 1.10/1.05 (~node4(s28)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2749, 388, 2686])).
% 1.10/1.05 tff(2751,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2752,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s28, s29)) | node7(s28, s29))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2753,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s28, s29)) | node7(s28, s29)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 1.10/1.05 tff(2754,plain,
% 1.10/1.05 (node7(s28, s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2753, 206, 2697])).
% 1.10/1.05 tff(2755,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2756,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2757,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.10/1.05 tff(2758,plain,
% 1.10/1.05 (m_main_v_state1(s28, c_c1) | node1(s28) | node2(s28) | node3(s28) | node4(s28) | node5(s28) | node6(s28, s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2757, 820, 2754])).
% 1.10/1.05 tff(2759,plain,
% 1.10/1.05 (node6(s28, s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2758, 2750, 2674, 2746, 2742, 2738, 2721])).
% 1.10/1.05 tff(2760,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2761,plain,
% 1.10/1.05 (((~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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2762,plain,
% 1.10/1.05 (((~![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))))),
% 1.10/1.05 inference(monotonicity,[status(thm)],[2761])).
% 1.10/1.05 tff(2763,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(transitivity,[status(thm)],[2762, 2760])).
% 1.10/1.05 tff(2764,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2765,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 1.10/1.05 tff(2766,plain,
% 1.10/1.05 (~m_main_v_state1(s29, c_n1)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2765, 835, 2666, 2759])).
% 1.10/1.05 tff(2767,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2768,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s29, c_n1) | (~node2(s29)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2769,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s29, c_n1) | (~node2(s29))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 1.10/1.05 tff(2770,plain,
% 1.10/1.05 (~node2(s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2769, 787, 2766])).
% 1.10/1.05 tff(2771,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2772,plain,
% 1.10/1.05 (((~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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2773,plain,
% 1.10/1.05 (((~![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))))),
% 1.10/1.05 inference(monotonicity,[status(thm)],[2772])).
% 1.10/1.05 tff(2774,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(transitivity,[status(thm)],[2773, 2771])).
% 1.10/1.05 tff(2775,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2776,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 1.10/1.05 tff(2777,plain,
% 1.10/1.05 (m_main_v_state1(s29, c_t1)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2776, 856, 2662, 2759])).
% 1.10/1.05 tff(2778,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2779,plain,
% 1.10/1.05 ((~![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)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2780,plain,
% 1.10/1.05 ((~![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))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2779, 2778])).
% 1.10/1.05 tff(2781,plain,
% 1.10/1.05 (~m_main_v_state2(s29, c_t2)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2780, 77, 2709])).
% 1.10/1.05 tff(2782,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2783,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s29, c_t2) | (~node1(s29)))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2784,plain,
% 1.10/1.05 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s29, c_t2) | (~node1(s29))),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 1.10/1.05 tff(2785,plain,
% 1.10/1.05 (~node1(s29)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2784, 195, 2781])).
% 1.10/1.05 tff(2786,plain,
% 1.10/1.05 (succ(s29, s30) <=> succ(s29, s30)),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2787,axiom,(succ(s29, s30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound30')).
% 1.10/1.05 tff(2788,plain,
% 1.10/1.05 (succ(s29, s30)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 1.10/1.05 tff(2789,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2790,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2791,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 1.10/1.05 tff(2792,plain,
% 1.10/1.05 (trans(s29, s30)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2791, 2788, 39])).
% 1.10/1.05 tff(2793,plain,
% 1.10/1.05 (((~![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))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2794,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s29, s30)) | node7(s29, s30))),
% 1.10/1.05 inference(quant_inst,[status(thm)],[])).
% 1.10/1.05 tff(2795,plain,
% 1.10/1.05 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s29, s30)) | node7(s29, s30)),
% 1.10/1.05 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 1.10/1.05 tff(2796,plain,
% 1.10/1.05 (node7(s29, s30)),
% 1.10/1.05 inference(unit_resolution,[status(thm)],[2795, 206, 2792])).
% 1.10/1.05 tff(2797,plain,
% 1.10/1.05 (((~![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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2798,plain,
% 1.10/1.05 (((~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)))),
% 1.10/1.05 inference(rewrite,[status(thm)],[])).
% 1.10/1.05 tff(2799,plain,
% 1.10/1.05 (((~![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))))),
% 1.10/1.06 inference(monotonicity,[status(thm)],[2798])).
% 1.10/1.06 tff(2800,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.10/1.06 tff(2801,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2802,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.10/1.06 tff(2803,plain,
% 1.10/1.06 ((~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)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2802, 892, 2796])).
% 1.10/1.06 tff(2804,plain,
% 1.10/1.06 (m_main_v_state1(s30, c_c1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2803, 2785, 2709, 2777, 2770, 2717])).
% 1.10/1.06 tff(2805,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2806,plain,
% 1.10/1.06 ((~![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)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2807,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 1.10/1.06 tff(2808,plain,
% 1.10/1.06 (~m_main_v_state1(s30, c_t1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2807, 539, 2804])).
% 1.10/1.06 tff(2809,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2810,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s30, c_t1) | (~node5(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2811,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s30, c_t1) | (~node5(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.10/1.06 tff(2812,plain,
% 1.10/1.06 (~node5(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2811, 550, 2808])).
% 1.10/1.06 tff(2813,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2814,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s29, s30)) | node14(s29, s30))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2815,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s29, s30)) | node14(s29, s30)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2814, 2813])).
% 1.10/1.06 tff(2816,plain,
% 1.10/1.06 (node14(s29, s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2815, 7, 2792])).
% 1.10/1.06 tff(2817,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2818,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2819,plain,
% 1.10/1.06 ((~![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)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 1.10/1.06 tff(2820,plain,
% 1.10/1.06 ((~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_state2(s30, c_t2)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2819, 922, 2816])).
% 1.10/1.06 tff(2821,plain,
% 1.10/1.06 (m_main_v_state2(s30, c_t2)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2820, 2777, 2709])).
% 1.10/1.06 tff(2822,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2823,plain,
% 1.10/1.06 ((~![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)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2824,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 1.10/1.06 tff(2825,plain,
% 1.10/1.06 (~m_main_v_state2(s30, c_n2)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2824, 77, 2821])).
% 1.10/1.06 tff(2826,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2827,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s30, c_n2) | (~node4(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2828,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s30, c_n2) | (~node4(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.10/1.06 tff(2829,plain,
% 1.10/1.06 (~node4(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2828, 388, 2825])).
% 1.10/1.06 tff(2830,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2831,plain,
% 1.10/1.06 ((~![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)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2832,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 1.10/1.06 tff(2833,plain,
% 1.10/1.06 (~m_main_v_state2(s30, c_c2)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2832, 260, 2821])).
% 1.10/1.06 tff(2834,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2835,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s30, c_c2) | (~node3(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2836,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s30, c_c2) | (~node3(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2835, 2834])).
% 1.10/1.06 tff(2837,plain,
% 1.10/1.06 (~node3(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2836, 399, 2833])).
% 1.10/1.06 tff(2838,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2839,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s30, c_n2) | (~node2(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2840,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s30, c_n2) | (~node2(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 1.10/1.06 tff(2841,plain,
% 1.10/1.06 (~node2(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2840, 410, 2825])).
% 1.10/1.06 tff(2842,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2843,plain,
% 1.10/1.06 ((~![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)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2844,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 1.10/1.06 tff(2845,plain,
% 1.10/1.06 (~m_main_v_state1(s30, c_n1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2844, 454, 2804])).
% 1.10/1.06 tff(2846,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2847,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s30, c_n1) | (~node1(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2848,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s30, c_n1) | (~node1(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.10/1.06 tff(2849,plain,
% 1.10/1.06 (~node1(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2848, 421, 2845])).
% 1.10/1.06 tff(2850,plain,
% 1.10/1.06 (succ(s30, s31) <=> succ(s30, s31)),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2851,axiom,(succ(s30, s31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 1.10/1.06 tff(2852,plain,
% 1.10/1.06 (succ(s30, s31)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 1.10/1.06 tff(2853,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2854,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2855,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 1.10/1.06 tff(2856,plain,
% 1.10/1.06 (trans(s30, s31)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2855, 2852, 39])).
% 1.10/1.06 tff(2857,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2858,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s30, s31)) | node7(s30, s31))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2859,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s30, s31)) | node7(s30, s31)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 1.10/1.06 tff(2860,plain,
% 1.10/1.06 (node7(s30, s31)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2859, 206, 2856])).
% 1.10/1.06 tff(2861,plain,
% 1.10/1.06 (((~![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(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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2862,plain,
% 1.10/1.06 (((~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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2863,plain,
% 1.10/1.06 (((~![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(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))))),
% 1.10/1.06 inference(monotonicity,[status(thm)],[2862])).
% 1.10/1.06 tff(2864,plain,
% 1.10/1.06 (((~![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(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)))),
% 1.10/1.06 inference(transitivity,[status(thm)],[2863, 2861])).
% 1.10/1.06 tff(2865,plain,
% 1.10/1.06 ((~![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(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31)) | m_main_v_state1(s31, c_n1))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2866,plain,
% 1.10/1.06 ((~![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(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30) | (~node7(s30, s31))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 1.10/1.06 tff(2867,plain,
% 1.10/1.06 (m_main_v_state1(s31, c_n1) | (~m_main_v_state1(s30, c_c1)) | node1(s30) | node2(s30) | node3(s30) | node4(s30) | node5(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2866, 584, 2860])).
% 1.10/1.06 tff(2868,plain,
% 1.10/1.06 (m_main_v_state1(s31, c_n1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2867, 2849, 2804, 2841, 2837, 2829, 2812])).
% 1.10/1.06 tff(2869,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2870,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s29, c_t2) | (~node15(s29)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2871,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s29, c_t2) | (~node15(s29))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 1.10/1.06 tff(2872,plain,
% 1.10/1.06 (~node15(s29)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2871, 103, 2781])).
% 1.10/1.06 tff(2873,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2874,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s29, s30)) | node18(s29, s30))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2875,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s29, s30)) | node18(s29, s30)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2874, 2873])).
% 1.10/1.06 tff(2876,plain,
% 1.10/1.06 (node18(s29, s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2875, 125, 2792])).
% 1.10/1.06 tff(2877,plain,
% 1.10/1.06 (((~![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(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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2878,plain,
% 1.10/1.06 (((~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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2879,plain,
% 1.10/1.06 (((~![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(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)))),
% 1.10/1.06 inference(monotonicity,[status(thm)],[2878])).
% 1.10/1.06 tff(2880,plain,
% 1.10/1.06 (((~![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(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))),
% 1.10/1.06 inference(transitivity,[status(thm)],[2879, 2877])).
% 1.10/1.06 tff(2881,plain,
% 1.10/1.06 ((~![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(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | node15(s29) | (~node18(s29, s30)) | m_main_v_turn(s30, c_1))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2882,plain,
% 1.10/1.06 ((~![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(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)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2881, 2880])).
% 1.10/1.06 tff(2883,plain,
% 1.10/1.06 (node15(s29) | (~m_main_v_state1(s29, c_t1)) | (~m_main_v_state2(s29, c_n2)) | m_main_v_turn(s30, c_1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2882, 992, 2876])).
% 1.10/1.06 tff(2884,plain,
% 1.10/1.06 (m_main_v_turn(s30, c_1)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2883, 2872, 2709, 2777])).
% 1.10/1.06 tff(2885,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2886,plain,
% 1.10/1.06 ((~![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)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2887,plain,
% 1.10/1.06 ((~![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))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 1.10/1.06 tff(2888,plain,
% 1.10/1.06 (~m_main_v_turn(s30, c_2)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2887, 156, 2884])).
% 1.10/1.06 tff(2889,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2890,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s30, c_2) | (~node12(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2891,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s30, c_2) | (~node12(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 1.10/1.06 tff(2892,plain,
% 1.10/1.06 (~node12(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2891, 184, 2888])).
% 1.10/1.06 tff(2893,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2894,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s30, c_n2) | (~node8(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2895,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s30, c_n2) | (~node8(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 1.10/1.06 tff(2896,plain,
% 1.10/1.06 (~node8(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2895, 271, 2825])).
% 1.10/1.06 tff(2897,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2898,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s30, c_n2) | (~node9(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2899,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s30, c_n2) | (~node9(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 1.10/1.06 tff(2900,plain,
% 1.10/1.06 (~node9(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2899, 88, 2825])).
% 1.10/1.06 tff(2901,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2902,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s30, c_n2) | (~node10(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2903,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s30, c_n2) | (~node10(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 1.10/1.06 tff(2904,plain,
% 1.10/1.06 (~node10(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2903, 249, 2825])).
% 1.10/1.06 tff(2905,plain,
% 1.10/1.06 (((~![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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2906,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s30, c_n1) | (~node11(s30)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2907,plain,
% 1.10/1.06 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s30, c_n1) | (~node11(s30))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 1.10/1.06 tff(2908,plain,
% 1.10/1.06 (~node11(s30)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2907, 238, 2845])).
% 1.10/1.06 tff(2909,plain,
% 1.10/1.06 (((~![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))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2910,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s30, s31)) | node14(s30, s31))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2911,plain,
% 1.10/1.06 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s30, s31)) | node14(s30, s31)),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 1.10/1.06 tff(2912,plain,
% 1.10/1.06 (node14(s30, s31)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2911, 7, 2856])).
% 1.10/1.06 tff(2913,plain,
% 1.10/1.06 (((~![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(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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2914,plain,
% 1.10/1.06 ((~![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(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31)))),
% 1.10/1.06 inference(quant_inst,[status(thm)],[])).
% 1.10/1.06 tff(2915,plain,
% 1.10/1.06 ((~![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(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31) | (~node14(s30, s31))),
% 1.10/1.06 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.10/1.06 tff(2916,plain,
% 1.10/1.06 (m_main_v_state2(s30, c_c2) | node9(s30) | node8(s30) | node10(s30) | node11(s30) | node12(s30) | node13(s30, s31)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2915, 296, 2912])).
% 1.10/1.06 tff(2917,plain,
% 1.10/1.06 (node13(s30, s31)),
% 1.10/1.06 inference(unit_resolution,[status(thm)],[2916, 2908, 2833, 2904, 2900, 2896, 2892])).
% 1.10/1.06 tff(2918,plain,
% 1.10/1.06 (((~![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(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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2919,plain,
% 1.10/1.06 (((~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)))),
% 1.10/1.06 inference(rewrite,[status(thm)],[])).
% 1.10/1.06 tff(2920,plain,
% 1.10/1.06 (((~![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))))),
% 1.10/1.07 inference(monotonicity,[status(thm)],[2919])).
% 1.10/1.07 tff(2921,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(transitivity,[status(thm)],[2920, 2918])).
% 1.10/1.07 tff(2922,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2923,plain,
% 1.10/1.07 ((~![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(s30, c_t2)) | m_main_v_state2(s31, c_t2) | (~node13(s30, s31))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 1.10/1.07 tff(2924,plain,
% 1.10/1.07 (m_main_v_state2(s31, c_t2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2923, 518, 2821, 2917])).
% 1.10/1.07 tff(2925,plain,
% 1.10/1.07 (succ(s31, s32) <=> succ(s31, s32)),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2926,axiom,(succ(s31, s32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound32')).
% 1.10/1.07 tff(2927,plain,
% 1.10/1.07 (succ(s31, s32)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.10/1.07 tff(2928,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2929,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2930,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.10/1.07 tff(2931,plain,
% 1.10/1.07 (trans(s31, s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2930, 2927, 39])).
% 1.10/1.07 tff(2932,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2933,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s31, s32)) | node7(s31, s32))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2934,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s31, s32)) | node7(s31, s32)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 1.10/1.07 tff(2935,plain,
% 1.10/1.07 (node7(s31, s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2934, 206, 2931])).
% 1.10/1.07 tff(2936,plain,
% 1.10/1.07 (((~![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(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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2937,plain,
% 1.10/1.07 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2938,plain,
% 1.10/1.07 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node7(s31, s32)) | m_main_v_state1(s32, c_t1)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.10/1.07 tff(2939,plain,
% 1.10/1.07 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_state1(s32, c_t1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2938, 651, 2935])).
% 1.10/1.07 tff(2940,plain,
% 1.10/1.07 (m_main_v_state1(s32, c_t1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2939, 2924, 2868])).
% 1.10/1.07 tff(2941,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2942,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2943,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.10/1.07 tff(2944,plain,
% 1.10/1.07 (~m_main_v_state1(s32, c_n1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2943, 17, 2940])).
% 1.10/1.07 tff(2945,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2946,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s32, c_n1) | (~node1(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2947,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s32, c_n1) | (~node1(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.10/1.07 tff(2948,plain,
% 1.10/1.07 (~node1(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2947, 421, 2944])).
% 1.10/1.07 tff(2949,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2950,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s31, s32)) | node18(s31, s32))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2951,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s31, s32)) | node18(s31, s32)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.10/1.07 tff(2952,plain,
% 1.10/1.07 (node18(s31, s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2951, 125, 2931])).
% 1.10/1.07 tff(2953,plain,
% 1.10/1.07 (((~![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(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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2954,plain,
% 1.10/1.07 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2955,plain,
% 1.10/1.07 ((~![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(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | (~node18(s31, s32)) | m_main_v_turn(s32, c_2)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 1.10/1.07 tff(2956,plain,
% 1.10/1.07 ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state2(s31, c_t2)) | m_main_v_turn(s32, c_2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2955, 760, 2952])).
% 1.10/1.07 tff(2957,plain,
% 1.10/1.07 (m_main_v_turn(s32, c_2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2956, 2924, 2868])).
% 1.10/1.07 tff(2958,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2959,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2960,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 1.10/1.07 tff(2961,plain,
% 1.10/1.07 (~m_main_v_turn(s32, c_1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2960, 156, 2957])).
% 1.10/1.07 tff(2962,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2963,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s32, c_1) | (~node5(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2964,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s32, c_1) | (~node5(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.10/1.07 tff(2965,plain,
% 1.10/1.07 (~node5(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2964, 776, 2961])).
% 1.10/1.07 tff(2966,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2967,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s32, c_n1) | (~node2(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2968,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s32, c_n1) | (~node2(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 1.10/1.07 tff(2969,plain,
% 1.10/1.07 (~node2(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2968, 787, 2944])).
% 1.10/1.07 tff(2970,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2971,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s32, c_n1) | (~node3(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2972,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s32, c_n1) | (~node3(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 1.10/1.07 tff(2973,plain,
% 1.10/1.07 (~node3(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2972, 798, 2944])).
% 1.10/1.07 tff(2974,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2975,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2976,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 1.10/1.07 tff(2977,plain,
% 1.10/1.07 (~m_main_v_state1(s32, c_c1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2976, 539, 2940])).
% 1.10/1.07 tff(2978,plain,
% 1.10/1.07 (((~![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(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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2979,plain,
% 1.10/1.07 (((~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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2980,plain,
% 1.10/1.07 (((~![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))))),
% 1.10/1.07 inference(monotonicity,[status(thm)],[2979])).
% 1.10/1.07 tff(2981,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(transitivity,[status(thm)],[2980, 2978])).
% 1.10/1.07 tff(2982,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2983,plain,
% 1.10/1.07 ((~![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(s30, c_n2) | (~m_main_v_state2(s31, c_n2)) | (~node13(s30, s31))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 1.10/1.07 tff(2984,plain,
% 1.10/1.07 (~m_main_v_state2(s31, c_n2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2983, 311, 2825, 2917])).
% 1.10/1.07 tff(2985,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2986,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s31, c_n2) | (~node9(s31)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2987,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s31, c_n2) | (~node9(s31))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2986, 2985])).
% 1.10/1.07 tff(2988,plain,
% 1.10/1.07 (~node9(s31)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2987, 88, 2984])).
% 1.10/1.07 tff(2989,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2990,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s31, c_n2) | (~node10(s31)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2991,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s31, c_n2) | (~node10(s31))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 1.10/1.07 tff(2992,plain,
% 1.10/1.07 (~node10(s31)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2991, 249, 2984])).
% 1.10/1.07 tff(2993,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2994,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s31, c_n2) | (~node8(s31)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2995,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s31, c_n2) | (~node8(s31))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 1.10/1.07 tff(2996,plain,
% 1.10/1.07 (~node8(s31)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2995, 271, 2984])).
% 1.10/1.07 tff(2997,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(2998,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s31, s32)) | node14(s31, s32))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(2999,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s31, s32)) | node14(s31, s32)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 1.10/1.07 tff(3000,plain,
% 1.10/1.07 (node14(s31, s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[2999, 7, 2931])).
% 1.10/1.07 tff(3001,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3002,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3003,plain,
% 1.10/1.07 ((~![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)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 1.10/1.07 tff(3004,plain,
% 1.10/1.07 ((~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)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3003, 617, 3000])).
% 1.10/1.07 tff(3005,plain,
% 1.10/1.07 (m_main_v_state2(s32, c_c2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3004, 2996, 2868, 2924, 2992, 2988])).
% 1.10/1.07 tff(3006,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3007,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3008,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.10/1.07 tff(3009,plain,
% 1.10/1.07 (~m_main_v_state2(s32, c_n2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3008, 697, 3005])).
% 1.10/1.07 tff(3010,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3011,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s32, c_n2) | (~node4(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3012,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s32, c_n2) | (~node4(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 1.10/1.07 tff(3013,plain,
% 1.10/1.07 (~node4(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3012, 388, 3009])).
% 1.10/1.07 tff(3014,plain,
% 1.10/1.07 (succ(s32, s33) <=> succ(s32, s33)),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3015,axiom,(succ(s32, s33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound33')).
% 1.10/1.07 tff(3016,plain,
% 1.10/1.07 (succ(s32, s33)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 1.10/1.07 tff(3017,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3018,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3019,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 1.10/1.07 tff(3020,plain,
% 1.10/1.07 (trans(s32, s33)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3019, 3016, 39])).
% 1.10/1.07 tff(3021,plain,
% 1.10/1.07 (((~![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))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3022,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s32, s33)) | node7(s32, s33))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3023,plain,
% 1.10/1.07 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s32, s33)) | node7(s32, s33)),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 1.10/1.07 tff(3024,plain,
% 1.10/1.07 (node7(s32, s33)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3023, 206, 3020])).
% 1.10/1.07 tff(3025,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3026,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3027,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3026, 3025])).
% 1.10/1.07 tff(3028,plain,
% 1.10/1.07 (m_main_v_state1(s32, c_c1) | node1(s32) | node2(s32) | node3(s32) | node4(s32) | node5(s32) | node6(s32, s33)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3027, 820, 3024])).
% 1.10/1.07 tff(3029,plain,
% 1.10/1.07 (node6(s32, s33)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3028, 3013, 2977, 2973, 2969, 2965, 2948])).
% 1.10/1.07 tff(3030,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3031,plain,
% 1.10/1.07 (((~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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3032,plain,
% 1.10/1.07 (((~![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))))),
% 1.10/1.07 inference(monotonicity,[status(thm)],[3031])).
% 1.10/1.07 tff(3033,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(transitivity,[status(thm)],[3032, 3030])).
% 1.10/1.07 tff(3034,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3035,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 1.10/1.07 tff(3036,plain,
% 1.10/1.07 (m_main_v_state1(s33, c_t1)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3035, 856, 2940, 3029])).
% 1.10/1.07 tff(3037,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3038,plain,
% 1.10/1.07 ((~![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)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3039,plain,
% 1.10/1.07 ((~![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))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3038, 3037])).
% 1.10/1.07 tff(3040,plain,
% 1.10/1.07 (~m_main_v_state2(s32, c_t2)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3039, 260, 3005])).
% 1.10/1.07 tff(3041,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3042,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s32, c_t2) | (~node12(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3043,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s32, c_t2) | (~node12(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 1.10/1.07 tff(3044,plain,
% 1.10/1.07 (~node12(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3043, 633, 3040])).
% 1.10/1.07 tff(3045,plain,
% 1.10/1.07 (((~![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)))),
% 1.10/1.07 inference(rewrite,[status(thm)],[])).
% 1.10/1.07 tff(3046,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s32, c_n1) | (~node11(s32)))),
% 1.10/1.07 inference(quant_inst,[status(thm)],[])).
% 1.10/1.07 tff(3047,plain,
% 1.10/1.07 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s32, c_n1) | (~node11(s32))),
% 1.10/1.07 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 1.10/1.07 tff(3048,plain,
% 1.10/1.07 (~node11(s32)),
% 1.10/1.07 inference(unit_resolution,[status(thm)],[3047, 238, 2944])).
% 1.10/1.08 tff(3049,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3050,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s32, c_c1) | (~node10(s32)))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3051,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s32, c_c1) | (~node10(s32))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 1.10/1.08 tff(3052,plain,
% 1.10/1.08 (~node10(s32)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3051, 675, 2977])).
% 1.10/1.08 tff(3053,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3054,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s32, c_n1) | (~node9(s32)))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3055,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s32, c_n1) | (~node9(s32))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 1.10/1.08 tff(3056,plain,
% 1.10/1.08 (~node9(s32)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3055, 686, 2944])).
% 1.10/1.08 tff(3057,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3058,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s32, c_n2) | (~node8(s32)))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3059,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s32, c_n2) | (~node8(s32))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 1.10/1.08 tff(3060,plain,
% 1.10/1.08 (~node8(s32)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3059, 271, 3009])).
% 1.10/1.08 tff(3061,plain,
% 1.10/1.08 (((~![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))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3062,plain,
% 1.10/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s32, s33)) | node14(s32, s33))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3063,plain,
% 1.10/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s32, s33)) | node14(s32, s33)),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 1.10/1.08 tff(3064,plain,
% 1.10/1.08 (node14(s32, s33)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3063, 7, 3020])).
% 1.10/1.08 tff(3065,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3066,plain,
% 1.10/1.08 (((~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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3067,plain,
% 1.10/1.08 (((~![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))))),
% 1.10/1.08 inference(monotonicity,[status(thm)],[3066])).
% 1.10/1.08 tff(3068,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(transitivity,[status(thm)],[3067, 3065])).
% 1.10/1.08 tff(3069,plain,
% 1.10/1.08 ((~![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))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3070,plain,
% 1.10/1.08 ((~![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))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 1.10/1.08 tff(3071,plain,
% 1.10/1.08 (m_main_v_state2(s33, c_n2) | node9(s32) | node8(s32) | node10(s32) | node11(s32) | node12(s32) | (~m_main_v_state2(s32, c_c2))),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3070, 726, 3064])).
% 1.10/1.08 tff(3072,plain,
% 1.10/1.08 (m_main_v_state2(s33, c_n2)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3071, 3060, 3005, 3056, 3052, 3048, 3044])).
% 1.10/1.08 tff(3073,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3074,plain,
% 1.10/1.08 ((~![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)))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3075,plain,
% 1.10/1.08 ((~![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))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 1.10/1.08 tff(3076,plain,
% 1.10/1.08 (~m_main_v_state2(s33, c_t2)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3075, 77, 3072])).
% 1.10/1.08 tff(3077,plain,
% 1.10/1.08 (((~![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)))),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.10/1.08 tff(3078,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s33, c_t2) | (~node15(s33)))),
% 1.10/1.08 inference(quant_inst,[status(thm)],[])).
% 1.10/1.08 tff(3079,plain,
% 1.10/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s33, c_t2) | (~node15(s33))),
% 1.10/1.08 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.10/1.08 tff(3080,plain,
% 1.10/1.08 (~node15(s33)),
% 1.10/1.08 inference(unit_resolution,[status(thm)],[3079, 103, 3076])).
% 1.10/1.08 tff(3081,plain,
% 1.10/1.08 (succ(s33, s34) <=> succ(s33, s34)),
% 1.10/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3082,axiom,(succ(s33, s34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound34')).
% 1.16/1.08 tff(3083,plain,
% 1.16/1.08 (succ(s33, s34)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 1.16/1.08 tff(3084,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3085,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3086,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.16/1.08 tff(3087,plain,
% 1.16/1.08 (trans(s33, s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3086, 3083, 39])).
% 1.16/1.08 tff(3088,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3089,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s33, s34)) | node18(s33, s34))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3090,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s33, s34)) | node18(s33, s34)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 1.16/1.08 tff(3091,plain,
% 1.16/1.08 (node18(s33, s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3090, 125, 3087])).
% 1.16/1.08 tff(3092,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3093,plain,
% 1.16/1.08 (((~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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3094,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(monotonicity,[status(thm)],[3093])).
% 1.16/1.08 tff(3095,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(transitivity,[status(thm)],[3094, 3092])).
% 1.16/1.08 tff(3096,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3097,plain,
% 1.16/1.08 ((~![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)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 1.16/1.08 tff(3098,plain,
% 1.16/1.08 (node15(s33) | (~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_turn(s34, c_1)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3097, 992, 3091])).
% 1.16/1.08 tff(3099,plain,
% 1.16/1.08 (m_main_v_turn(s34, c_1)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3098, 3080, 3072, 3036])).
% 1.16/1.08 tff(3100,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3101,plain,
% 1.16/1.08 ((~![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)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3102,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 1.16/1.08 tff(3103,plain,
% 1.16/1.08 (~m_main_v_turn(s34, c_2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3102, 156, 3099])).
% 1.16/1.08 tff(3104,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3105,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s34, c_2) | (~node12(s34)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3106,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s34, c_2) | (~node12(s34))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 1.16/1.08 tff(3107,plain,
% 1.16/1.08 (~node12(s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3106, 184, 3103])).
% 1.16/1.08 tff(3108,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3109,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s33, s34)) | node14(s33, s34))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3110,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s33, s34)) | node14(s33, s34)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3109, 3108])).
% 1.16/1.08 tff(3111,plain,
% 1.16/1.08 (node14(s33, s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3110, 7, 3087])).
% 1.16/1.08 tff(3112,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3113,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3114,plain,
% 1.16/1.08 ((~![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)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 1.16/1.08 tff(3115,plain,
% 1.16/1.08 ((~m_main_v_state1(s33, c_t1)) | (~m_main_v_state2(s33, c_n2)) | m_main_v_state2(s34, c_t2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3114, 922, 3111])).
% 1.16/1.08 tff(3116,plain,
% 1.16/1.08 (m_main_v_state2(s34, c_t2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3115, 3036, 3072])).
% 1.16/1.08 tff(3117,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3118,plain,
% 1.16/1.08 ((~![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)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3119,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 1.16/1.08 tff(3120,plain,
% 1.16/1.08 (~m_main_v_state2(s34, c_n2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3119, 77, 3116])).
% 1.16/1.08 tff(3121,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3122,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s34, c_n2) | (~node8(s34)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3123,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s34, c_n2) | (~node8(s34))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 1.16/1.08 tff(3124,plain,
% 1.16/1.08 (~node8(s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3123, 271, 3120])).
% 1.16/1.08 tff(3125,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3126,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s34, c_n2) | (~node9(s34)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3127,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s34, c_n2) | (~node9(s34))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 1.16/1.08 tff(3128,plain,
% 1.16/1.08 (~node9(s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3127, 88, 3120])).
% 1.16/1.08 tff(3129,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3130,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s34, c_n2) | (~node10(s34)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3131,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s34, c_n2) | (~node10(s34))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 1.16/1.08 tff(3132,plain,
% 1.16/1.08 (~node10(s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3131, 249, 3120])).
% 1.16/1.08 tff(3133,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3134,plain,
% 1.16/1.08 ((~![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)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3135,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 1.16/1.08 tff(3136,plain,
% 1.16/1.08 (~m_main_v_state2(s34, c_c2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3135, 260, 3116])).
% 1.16/1.08 tff(3137,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3138,plain,
% 1.16/1.08 ((~![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)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3139,plain,
% 1.16/1.08 ((~![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))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3138, 3137])).
% 1.16/1.08 tff(3140,plain,
% 1.16/1.08 (~m_main_v_state2(s33, c_c2)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3139, 697, 3072])).
% 1.16/1.08 tff(3141,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3142,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s33, c_c2) | (~node3(s33)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3143,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s33, c_c2) | (~node3(s33))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 1.16/1.08 tff(3144,plain,
% 1.16/1.08 (~node3(s33)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3143, 399, 3140])).
% 1.16/1.08 tff(3145,plain,
% 1.16/1.08 (((~![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(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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3146,plain,
% 1.16/1.08 (((~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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3147,plain,
% 1.16/1.08 (((~![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))))),
% 1.16/1.08 inference(monotonicity,[status(thm)],[3146])).
% 1.16/1.08 tff(3148,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(transitivity,[status(thm)],[3147, 3145])).
% 1.16/1.08 tff(3149,plain,
% 1.16/1.08 ((~![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)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3150,plain,
% 1.16/1.08 ((~![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(s32, c_n1) | (~m_main_v_state1(s33, c_n1)) | (~node6(s32, s33))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.16/1.08 tff(3151,plain,
% 1.16/1.08 (~m_main_v_state1(s33, c_n1)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3150, 835, 2944, 3029])).
% 1.16/1.08 tff(3152,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3153,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s33, c_n1) | (~node2(s33)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3154,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s33, c_n1) | (~node2(s33))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.16/1.08 tff(3155,plain,
% 1.16/1.08 (~node2(s33)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3154, 787, 3151])).
% 1.16/1.08 tff(3156,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3157,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s33, c_t2) | (~node1(s33)))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3158,plain,
% 1.16/1.08 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s33, c_t2) | (~node1(s33))),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.16/1.08 tff(3159,plain,
% 1.16/1.08 (~node1(s33)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3158, 195, 3076])).
% 1.16/1.08 tff(3160,plain,
% 1.16/1.08 (((~![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))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3161,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s33, s34)) | node7(s33, s34))),
% 1.16/1.08 inference(quant_inst,[status(thm)],[])).
% 1.16/1.08 tff(3162,plain,
% 1.16/1.08 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s33, s34)) | node7(s33, s34)),
% 1.16/1.08 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 1.16/1.08 tff(3163,plain,
% 1.16/1.08 (node7(s33, s34)),
% 1.16/1.08 inference(unit_resolution,[status(thm)],[3162, 206, 3087])).
% 1.16/1.08 tff(3164,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3165,plain,
% 1.16/1.08 (((~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)))),
% 1.16/1.08 inference(rewrite,[status(thm)],[])).
% 1.16/1.08 tff(3166,plain,
% 1.16/1.08 (((~![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))))),
% 1.16/1.08 inference(monotonicity,[status(thm)],[3165])).
% 1.16/1.08 tff(3167,plain,
% 1.16/1.08 (((~![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)))),
% 1.16/1.09 inference(transitivity,[status(thm)],[3166, 3164])).
% 1.16/1.09 tff(3168,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3169,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 1.16/1.09 tff(3170,plain,
% 1.16/1.09 ((~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)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3169, 892, 3163])).
% 1.16/1.09 tff(3171,plain,
% 1.16/1.09 (m_main_v_state1(s34, c_c1)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3170, 3159, 3072, 3036, 3155, 3144])).
% 1.16/1.09 tff(3172,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3173,plain,
% 1.16/1.09 ((~![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)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3174,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 1.16/1.09 tff(3175,plain,
% 1.16/1.09 (~m_main_v_state1(s34, c_n1)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3174, 454, 3171])).
% 1.16/1.09 tff(3176,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3177,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s34, c_n1) | (~node11(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3178,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s34, c_n1) | (~node11(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 1.16/1.09 tff(3179,plain,
% 1.16/1.09 (~node11(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3178, 238, 3175])).
% 1.16/1.09 tff(3180,plain,
% 1.16/1.09 (succ(s34, s35) <=> succ(s34, s35)),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3181,axiom,(succ(s34, s35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound35')).
% 1.16/1.09 tff(3182,plain,
% 1.16/1.09 (succ(s34, s35)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 1.16/1.09 tff(3183,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3184,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3185,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 1.16/1.09 tff(3186,plain,
% 1.16/1.09 (trans(s34, s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3185, 3182, 39])).
% 1.16/1.09 tff(3187,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3188,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s34, s35)) | node14(s34, s35))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3189,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s34, s35)) | node14(s34, s35)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 1.16/1.09 tff(3190,plain,
% 1.16/1.09 (node14(s34, s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3189, 7, 3186])).
% 1.16/1.09 tff(3191,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3192,plain,
% 1.16/1.09 ((~![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)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3193,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3192, 3191])).
% 1.16/1.09 tff(3194,plain,
% 1.16/1.09 (m_main_v_state2(s34, c_c2) | node9(s34) | node8(s34) | node10(s34) | node11(s34) | node12(s34) | node13(s34, s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3193, 296, 3190])).
% 1.16/1.09 tff(3195,plain,
% 1.16/1.09 (node13(s34, s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3194, 3179, 3136, 3132, 3128, 3124, 3107])).
% 1.16/1.09 tff(3196,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3197,plain,
% 1.16/1.09 (((~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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3198,plain,
% 1.16/1.09 (((~![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))))),
% 1.16/1.09 inference(monotonicity,[status(thm)],[3197])).
% 1.16/1.09 tff(3199,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(transitivity,[status(thm)],[3198, 3196])).
% 1.16/1.09 tff(3200,plain,
% 1.16/1.09 ((~![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)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3201,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 1.16/1.09 tff(3202,plain,
% 1.16/1.09 (~m_main_v_state2(s35, c_n2)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3201, 311, 3120, 3195])).
% 1.16/1.09 tff(3203,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3204,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s35, c_n2) | (~node9(s35)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3205,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s35, c_n2) | (~node9(s35))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.16/1.09 tff(3206,plain,
% 1.16/1.09 (~node9(s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3205, 88, 3202])).
% 1.16/1.09 tff(3207,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3208,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s35, c_n2) | (~node10(s35)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3209,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s35, c_n2) | (~node10(s35))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 1.16/1.09 tff(3210,plain,
% 1.16/1.09 (~node10(s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3209, 249, 3202])).
% 1.16/1.09 tff(3211,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3212,plain,
% 1.16/1.09 (((~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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3213,plain,
% 1.16/1.09 (((~![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))))),
% 1.16/1.09 inference(monotonicity,[status(thm)],[3212])).
% 1.16/1.09 tff(3214,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(transitivity,[status(thm)],[3213, 3211])).
% 1.16/1.09 tff(3215,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3216,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 1.16/1.09 tff(3217,plain,
% 1.16/1.09 (m_main_v_state2(s35, c_t2)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3216, 518, 3116, 3195])).
% 1.16/1.09 tff(3218,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3219,plain,
% 1.16/1.09 ((~![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)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3220,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.16/1.09 tff(3221,plain,
% 1.16/1.09 (~m_main_v_state1(s34, c_t1)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3220, 539, 3171])).
% 1.16/1.09 tff(3222,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3223,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s34, c_t1) | (~node5(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3224,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s34, c_t1) | (~node5(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 1.16/1.09 tff(3225,plain,
% 1.16/1.09 (~node5(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3224, 550, 3221])).
% 1.16/1.09 tff(3226,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3227,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s34, c_n2) | (~node4(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3228,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s34, c_n2) | (~node4(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 1.16/1.09 tff(3229,plain,
% 1.16/1.09 (~node4(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3228, 388, 3120])).
% 1.16/1.09 tff(3230,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3231,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s34, c_c2) | (~node3(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3232,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s34, c_c2) | (~node3(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3231, 3230])).
% 1.16/1.09 tff(3233,plain,
% 1.16/1.09 (~node3(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3232, 399, 3136])).
% 1.16/1.09 tff(3234,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3235,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s34, c_n2) | (~node2(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3236,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s34, c_n2) | (~node2(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.16/1.09 tff(3237,plain,
% 1.16/1.09 (~node2(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3236, 410, 3120])).
% 1.16/1.09 tff(3238,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3239,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s34, c_n1) | (~node1(s34)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3240,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s34, c_n1) | (~node1(s34))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 1.16/1.09 tff(3241,plain,
% 1.16/1.09 (~node1(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3240, 421, 3175])).
% 1.16/1.09 tff(3242,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3243,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s34, s35)) | node7(s34, s35))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3244,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s34, s35)) | node7(s34, s35)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 1.16/1.09 tff(3245,plain,
% 1.16/1.09 (node7(s34, s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3244, 206, 3186])).
% 1.16/1.09 tff(3246,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3247,plain,
% 1.16/1.09 (((~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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3248,plain,
% 1.16/1.09 (((~![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))))),
% 1.16/1.09 inference(monotonicity,[status(thm)],[3247])).
% 1.16/1.09 tff(3249,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(transitivity,[status(thm)],[3248, 3246])).
% 1.16/1.09 tff(3250,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3251,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 1.16/1.09 tff(3252,plain,
% 1.16/1.09 (m_main_v_state1(s35, c_n1) | (~m_main_v_state1(s34, c_c1)) | node1(s34) | node2(s34) | node3(s34) | node4(s34) | node5(s34)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3251, 584, 3245])).
% 1.16/1.09 tff(3253,plain,
% 1.16/1.09 (m_main_v_state1(s35, c_n1)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3252, 3241, 3171, 3237, 3233, 3229, 3225])).
% 1.16/1.09 tff(3254,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3255,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s35, c_n2) | (~node8(s35)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3256,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s35, c_n2) | (~node8(s35))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 1.16/1.09 tff(3257,plain,
% 1.16/1.09 (~node8(s35)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3256, 271, 3202])).
% 1.16/1.09 tff(3258,plain,
% 1.16/1.09 (succ(s35, s36) <=> succ(s35, s36)),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3259,axiom,(succ(s35, s36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound36')).
% 1.16/1.09 tff(3260,plain,
% 1.16/1.09 (succ(s35, s36)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3259, 3258])).
% 1.16/1.09 tff(3261,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3262,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3263,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 1.16/1.09 tff(3264,plain,
% 1.16/1.09 (trans(s35, s36)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3263, 3260, 39])).
% 1.16/1.09 tff(3265,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3266,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s35, s36)) | node14(s35, s36))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3267,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s35, s36)) | node14(s35, s36)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 1.16/1.09 tff(3268,plain,
% 1.16/1.09 (node14(s35, s36)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3267, 7, 3264])).
% 1.16/1.09 tff(3269,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3270,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3271,plain,
% 1.16/1.09 ((~![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)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 1.16/1.09 tff(3272,plain,
% 1.16/1.09 ((~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)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3271, 617, 3268])).
% 1.16/1.09 tff(3273,plain,
% 1.16/1.09 (m_main_v_state2(s36, c_c2)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3272, 3257, 3253, 3217, 3210, 3206])).
% 1.16/1.09 tff(3274,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3275,plain,
% 1.16/1.09 ((~![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)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3276,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 1.16/1.09 tff(3277,plain,
% 1.16/1.09 (~m_main_v_state2(s36, c_t2)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3276, 260, 3273])).
% 1.16/1.09 tff(3278,plain,
% 1.16/1.09 (((~![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)))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3279,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s36, c_t2) | (~node12(s36)))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3280,plain,
% 1.16/1.09 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s36, c_t2) | (~node12(s36))),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 1.16/1.09 tff(3281,plain,
% 1.16/1.09 (~node12(s36)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3280, 633, 3277])).
% 1.16/1.09 tff(3282,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3283,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s35, s36)) | node7(s35, s36))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3284,plain,
% 1.16/1.09 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s35, s36)) | node7(s35, s36)),
% 1.16/1.09 inference(modus_ponens,[status(thm)],[3283, 3282])).
% 1.16/1.09 tff(3285,plain,
% 1.16/1.09 (node7(s35, s36)),
% 1.16/1.09 inference(unit_resolution,[status(thm)],[3284, 206, 3264])).
% 1.16/1.09 tff(3286,plain,
% 1.16/1.09 (((~![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))),
% 1.16/1.09 inference(rewrite,[status(thm)],[])).
% 1.16/1.09 tff(3287,plain,
% 1.16/1.09 ((~![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))),
% 1.16/1.09 inference(quant_inst,[status(thm)],[])).
% 1.16/1.09 tff(3288,plain,
% 1.16/1.09 ((~![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)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 1.16/1.10 tff(3289,plain,
% 1.16/1.10 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_state1(s36, c_t1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3288, 651, 3285])).
% 1.16/1.10 tff(3290,plain,
% 1.16/1.10 (m_main_v_state1(s36, c_t1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3289, 3217, 3253])).
% 1.16/1.10 tff(3291,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3292,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3293,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 1.16/1.10 tff(3294,plain,
% 1.16/1.10 (~m_main_v_state1(s36, c_n1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3293, 17, 3290])).
% 1.16/1.10 tff(3295,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3296,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s36, c_n1) | (~node11(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3297,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s36, c_n1) | (~node11(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 1.16/1.10 tff(3298,plain,
% 1.16/1.10 (~node11(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3297, 238, 3294])).
% 1.16/1.10 tff(3299,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3300,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3301,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.16/1.10 tff(3302,plain,
% 1.16/1.10 (~m_main_v_state1(s36, c_c1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3301, 539, 3290])).
% 1.16/1.10 tff(3303,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3304,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s36, c_c1) | (~node10(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3305,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s36, c_c1) | (~node10(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3304, 3303])).
% 1.16/1.10 tff(3306,plain,
% 1.16/1.10 (~node10(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3305, 675, 3302])).
% 1.16/1.10 tff(3307,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3308,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s36, c_n1) | (~node9(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3309,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s36, c_n1) | (~node9(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.16/1.10 tff(3310,plain,
% 1.16/1.10 (~node9(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3309, 686, 3294])).
% 1.16/1.10 tff(3311,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3312,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3313,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3312, 3311])).
% 1.16/1.10 tff(3314,plain,
% 1.16/1.10 (~m_main_v_state2(s36, c_n2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3313, 697, 3273])).
% 1.16/1.10 tff(3315,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3316,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s36, c_n2) | (~node8(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3317,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s36, c_n2) | (~node8(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 1.16/1.10 tff(3318,plain,
% 1.16/1.10 (~node8(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3317, 271, 3314])).
% 1.16/1.10 tff(3319,plain,
% 1.16/1.10 (succ(s36, s37) <=> succ(s36, s37)),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3320,axiom,(succ(s36, s37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound37')).
% 1.16/1.10 tff(3321,plain,
% 1.16/1.10 (succ(s36, s37)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 1.16/1.10 tff(3322,plain,
% 1.16/1.10 (((~![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))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3323,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3324,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 1.16/1.10 tff(3325,plain,
% 1.16/1.10 (trans(s36, s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3324, 3321, 39])).
% 1.16/1.10 tff(3326,plain,
% 1.16/1.10 (((~![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))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3327,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s36, s37)) | node14(s36, s37))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3328,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s36, s37)) | node14(s36, s37)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 1.16/1.10 tff(3329,plain,
% 1.16/1.10 (node14(s36, s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3328, 7, 3325])).
% 1.16/1.10 tff(3330,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3331,plain,
% 1.16/1.10 (((~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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3332,plain,
% 1.16/1.10 (((~![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))))),
% 1.16/1.10 inference(monotonicity,[status(thm)],[3331])).
% 1.16/1.10 tff(3333,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(transitivity,[status(thm)],[3332, 3330])).
% 1.16/1.10 tff(3334,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3335,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 1.16/1.10 tff(3336,plain,
% 1.16/1.10 (m_main_v_state2(s37, c_n2) | node9(s36) | node8(s36) | node10(s36) | node11(s36) | node12(s36) | (~m_main_v_state2(s36, c_c2))),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3335, 726, 3329])).
% 1.16/1.10 tff(3337,plain,
% 1.16/1.10 (m_main_v_state2(s37, c_n2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3336, 3318, 3273, 3310, 3306, 3298, 3281])).
% 1.16/1.10 tff(3338,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3339,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3340,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 1.16/1.10 tff(3341,plain,
% 1.16/1.10 (~m_main_v_state2(s37, c_c2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3340, 697, 3337])).
% 1.16/1.10 tff(3342,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3343,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s37, c_c2) | (~node3(s37)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3344,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s37, c_c2) | (~node3(s37))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 1.16/1.10 tff(3345,plain,
% 1.16/1.10 (~node3(s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3344, 399, 3341])).
% 1.16/1.10 tff(3346,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3347,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s36, c_n1) | (~node1(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3348,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s36, c_n1) | (~node1(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 1.16/1.10 tff(3349,plain,
% 1.16/1.10 (~node1(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3348, 421, 3294])).
% 1.16/1.10 tff(3350,plain,
% 1.16/1.10 (((~![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))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3351,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s35, s36)) | node18(s35, s36))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3352,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s35, s36)) | node18(s35, s36)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.16/1.10 tff(3353,plain,
% 1.16/1.10 (node18(s35, s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3352, 125, 3264])).
% 1.16/1.10 tff(3354,plain,
% 1.16/1.10 (((~![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))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3355,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3356,plain,
% 1.16/1.10 ((~![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)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.16/1.10 tff(3357,plain,
% 1.16/1.10 ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state2(s35, c_t2)) | m_main_v_turn(s36, c_2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3356, 760, 3353])).
% 1.16/1.10 tff(3358,plain,
% 1.16/1.10 (m_main_v_turn(s36, c_2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3357, 3217, 3253])).
% 1.16/1.10 tff(3359,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3360,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3361,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 1.16/1.10 tff(3362,plain,
% 1.16/1.10 (~m_main_v_turn(s36, c_1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3361, 156, 3358])).
% 1.16/1.10 tff(3363,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3364,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s36, c_1) | (~node5(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3365,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s36, c_1) | (~node5(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3364, 3363])).
% 1.16/1.10 tff(3366,plain,
% 1.16/1.10 (~node5(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3365, 776, 3362])).
% 1.16/1.10 tff(3367,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3368,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s36, c_n1) | (~node2(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3369,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s36, c_n1) | (~node2(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3368, 3367])).
% 1.16/1.10 tff(3370,plain,
% 1.16/1.10 (~node2(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3369, 787, 3294])).
% 1.16/1.10 tff(3371,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3372,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s36, c_n1) | (~node3(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3373,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s36, c_n1) | (~node3(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.16/1.10 tff(3374,plain,
% 1.16/1.10 (~node3(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3373, 798, 3294])).
% 1.16/1.10 tff(3375,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3376,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s36, c_n2) | (~node4(s36)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3377,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s36, c_n2) | (~node4(s36))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3376, 3375])).
% 1.16/1.10 tff(3378,plain,
% 1.16/1.10 (~node4(s36)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3377, 388, 3314])).
% 1.16/1.10 tff(3379,plain,
% 1.16/1.10 (((~![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))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3380,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s36, s37)) | node7(s36, s37))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3381,plain,
% 1.16/1.10 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s36, s37)) | node7(s36, s37)),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 1.16/1.10 tff(3382,plain,
% 1.16/1.10 (node7(s36, s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3381, 206, 3325])).
% 1.16/1.10 tff(3383,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3384,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3385,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.16/1.10 tff(3386,plain,
% 1.16/1.10 (m_main_v_state1(s36, c_c1) | node1(s36) | node2(s36) | node3(s36) | node4(s36) | node5(s36) | node6(s36, s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3385, 820, 3382])).
% 1.16/1.10 tff(3387,plain,
% 1.16/1.10 (node6(s36, s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3386, 3378, 3302, 3374, 3370, 3366, 3349])).
% 1.16/1.10 tff(3388,plain,
% 1.16/1.10 (((~![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(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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3389,plain,
% 1.16/1.10 (((~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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3390,plain,
% 1.16/1.10 (((~![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))))),
% 1.16/1.10 inference(monotonicity,[status(thm)],[3389])).
% 1.16/1.10 tff(3391,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(transitivity,[status(thm)],[3390, 3388])).
% 1.16/1.10 tff(3392,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3393,plain,
% 1.16/1.10 ((~![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(s36, c_n1) | (~m_main_v_state1(s37, c_n1)) | (~node6(s36, s37))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 1.16/1.10 tff(3394,plain,
% 1.16/1.10 (~m_main_v_state1(s37, c_n1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3393, 835, 3294, 3387])).
% 1.16/1.10 tff(3395,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3396,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s37, c_n1) | (~node2(s37)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3397,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s37, c_n1) | (~node2(s37))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 1.16/1.10 tff(3398,plain,
% 1.16/1.10 (~node2(s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3397, 787, 3394])).
% 1.16/1.10 tff(3399,plain,
% 1.16/1.10 (((~![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(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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3400,plain,
% 1.16/1.10 (((~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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3401,plain,
% 1.16/1.10 (((~![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))))),
% 1.16/1.10 inference(monotonicity,[status(thm)],[3400])).
% 1.16/1.10 tff(3402,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(transitivity,[status(thm)],[3401, 3399])).
% 1.16/1.10 tff(3403,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3404,plain,
% 1.16/1.10 ((~![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(s36, c_t1)) | m_main_v_state1(s37, c_t1) | (~node6(s36, s37))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 1.16/1.10 tff(3405,plain,
% 1.16/1.10 (m_main_v_state1(s37, c_t1)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3404, 856, 3290, 3387])).
% 1.16/1.10 tff(3406,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3407,plain,
% 1.16/1.10 ((~![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)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3408,plain,
% 1.16/1.10 ((~![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))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 1.16/1.10 tff(3409,plain,
% 1.16/1.10 (~m_main_v_state2(s37, c_t2)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3408, 77, 3337])).
% 1.16/1.10 tff(3410,plain,
% 1.16/1.10 (((~![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)))),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3411,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s37, c_t2) | (~node1(s37)))),
% 1.16/1.10 inference(quant_inst,[status(thm)],[])).
% 1.16/1.10 tff(3412,plain,
% 1.16/1.10 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s37, c_t2) | (~node1(s37))),
% 1.16/1.10 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 1.16/1.10 tff(3413,plain,
% 1.16/1.10 (~node1(s37)),
% 1.16/1.10 inference(unit_resolution,[status(thm)],[3412, 195, 3409])).
% 1.16/1.10 tff(3414,plain,
% 1.16/1.10 (succ(s37, s38) <=> succ(s37, s38)),
% 1.16/1.10 inference(rewrite,[status(thm)],[])).
% 1.16/1.10 tff(3415,axiom,(succ(s37, s38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound38')).
% 1.16/1.10 tff(3416,plain,
% 1.16/1.11 (succ(s37, s38)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 1.16/1.11 tff(3417,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3418,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3419,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3418, 3417])).
% 1.16/1.11 tff(3420,plain,
% 1.16/1.11 (trans(s37, s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3419, 3416, 39])).
% 1.16/1.11 tff(3421,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3422,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s37, s38)) | node7(s37, s38))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3423,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s37, s38)) | node7(s37, s38)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.16/1.11 tff(3424,plain,
% 1.16/1.11 (node7(s37, s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3423, 206, 3420])).
% 1.16/1.11 tff(3425,plain,
% 1.16/1.11 (((~![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(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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3426,plain,
% 1.16/1.11 (((~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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3427,plain,
% 1.16/1.11 (((~![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(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))))),
% 1.16/1.11 inference(monotonicity,[status(thm)],[3426])).
% 1.16/1.11 tff(3428,plain,
% 1.16/1.11 (((~![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(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)))),
% 1.16/1.11 inference(transitivity,[status(thm)],[3427, 3425])).
% 1.16/1.11 tff(3429,plain,
% 1.16/1.11 ((~![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(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))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3430,plain,
% 1.16/1.11 ((~![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(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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 1.16/1.11 tff(3431,plain,
% 1.16/1.11 ((~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)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3430, 892, 3424])).
% 1.16/1.11 tff(3432,plain,
% 1.16/1.11 (m_main_v_state1(s38, c_c1)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3431, 3413, 3337, 3405, 3398, 3345])).
% 1.16/1.11 tff(3433,plain,
% 1.16/1.11 (^[X: $i] : refl(((~m_main_v_state1(X, c_c1)) | (~always19(X))) <=> ((~m_main_v_state1(X, c_c1)) | (~always19(X))))),
% 1.16/1.11 inference(bind,[status(th)],[])).
% 1.16/1.11 tff(3434,plain,
% 1.16/1.11 (![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X))) <=> ![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))),
% 1.16/1.11 inference(quant_intro,[status(thm)],[3433])).
% 1.16/1.11 tff(3435,plain,
% 1.16/1.11 (![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X))) <=> ![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3436,axiom,(![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 1.16/1.11 tff(3437,plain,
% 1.16/1.11 (![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.16/1.11 tff(3438,plain,(
% 1.16/1.11 ![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))),
% 1.16/1.11 inference(skolemize,[status(sab)],[3437])).
% 1.16/1.11 tff(3439,plain,
% 1.16/1.11 (![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3438, 3434])).
% 1.16/1.11 tff(3440,plain,
% 1.16/1.11 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s38)) | (~m_main_v_state1(s38, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s38)) | (~m_main_v_state1(s38, c_c1)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3441,plain,
% 1.16/1.11 (((~m_main_v_state1(s38, c_c1)) | (~always19(s38))) <=> ((~always19(s38)) | (~m_main_v_state1(s38, c_c1)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3442,plain,
% 1.16/1.11 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s38, c_c1)) | (~always19(s38)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s38)) | (~m_main_v_state1(s38, c_c1))))),
% 1.16/1.11 inference(monotonicity,[status(thm)],[3441])).
% 1.16/1.11 tff(3443,plain,
% 1.16/1.11 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s38, c_c1)) | (~always19(s38)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s38)) | (~m_main_v_state1(s38, c_c1)))),
% 1.16/1.11 inference(transitivity,[status(thm)],[3442, 3440])).
% 1.16/1.11 tff(3444,plain,
% 1.16/1.11 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s38, c_c1)) | (~always19(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3445,plain,
% 1.16/1.11 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s38)) | (~m_main_v_state1(s38, c_c1))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 1.16/1.11 tff(3446,plain,
% 1.16/1.11 (~always19(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3445, 3439, 3432])).
% 1.16/1.11 tff(3447,assumption,(~node20(s104)), introduced(assumption)).
% 1.16/1.11 tff(3448,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3449,plain,
% 1.16/1.11 ((~![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)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3450,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 1.16/1.11 tff(3451,plain,
% 1.16/1.11 (~m_main_v_state1(s38, c_t1)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3450, 539, 3432])).
% 1.16/1.11 tff(3452,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3453,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s38, c_t1) | (~node5(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3454,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s38, c_t1) | (~node5(s38))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 1.16/1.11 tff(3455,plain,
% 1.16/1.11 (~node5(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3454, 550, 3451])).
% 1.16/1.11 tff(3456,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3457,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s37, s38)) | node14(s37, s38))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3458,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s37, s38)) | node14(s37, s38)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 1.16/1.11 tff(3459,plain,
% 1.16/1.11 (node14(s37, s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3458, 7, 3420])).
% 1.16/1.11 tff(3460,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3461,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3462,plain,
% 1.16/1.11 ((~![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)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 1.16/1.11 tff(3463,plain,
% 1.16/1.11 ((~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_state2(s38, c_t2)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3462, 922, 3459])).
% 1.16/1.11 tff(3464,plain,
% 1.16/1.11 (m_main_v_state2(s38, c_t2)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3463, 3405, 3337])).
% 1.16/1.11 tff(3465,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3466,plain,
% 1.16/1.11 ((~![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)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3467,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 1.16/1.11 tff(3468,plain,
% 1.16/1.11 (~m_main_v_state2(s38, c_n2)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3467, 77, 3464])).
% 1.16/1.11 tff(3469,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3470,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s38, c_n2) | (~node4(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3471,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s38, c_n2) | (~node4(s38))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 1.16/1.11 tff(3472,plain,
% 1.16/1.11 (~node4(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3471, 388, 3468])).
% 1.16/1.11 tff(3473,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3474,plain,
% 1.16/1.11 ((~![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)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3475,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 1.16/1.11 tff(3476,plain,
% 1.16/1.11 (~m_main_v_state2(s38, c_c2)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3475, 260, 3464])).
% 1.16/1.11 tff(3477,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3478,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s38, c_c2) | (~node3(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3479,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s38, c_c2) | (~node3(s38))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 1.16/1.11 tff(3480,plain,
% 1.16/1.11 (~node3(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3479, 399, 3476])).
% 1.16/1.11 tff(3481,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3482,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s38, c_n2) | (~node2(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3483,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s38, c_n2) | (~node2(s38))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 1.16/1.11 tff(3484,plain,
% 1.16/1.11 (~node2(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3483, 410, 3468])).
% 1.16/1.11 tff(3485,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3486,plain,
% 1.16/1.11 ((~![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)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3487,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.16/1.11 tff(3488,plain,
% 1.16/1.11 (~m_main_v_state1(s38, c_n1)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3487, 454, 3432])).
% 1.16/1.11 tff(3489,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3490,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s38, c_n1) | (~node1(s38)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3491,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s38, c_n1) | (~node1(s38))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3490, 3489])).
% 1.16/1.11 tff(3492,plain,
% 1.16/1.11 (~node1(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3491, 421, 3488])).
% 1.16/1.11 tff(3493,plain,
% 1.16/1.11 (succ(s38, s39) <=> succ(s38, s39)),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3494,axiom,(succ(s38, s39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound39')).
% 1.16/1.11 tff(3495,plain,
% 1.16/1.11 (succ(s38, s39)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 1.16/1.11 tff(3496,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3497,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3498,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 1.16/1.11 tff(3499,plain,
% 1.16/1.11 (trans(s38, s39)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3498, 3495, 39])).
% 1.16/1.11 tff(3500,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3501,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s38, s39)) | node7(s38, s39))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3502,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s38, s39)) | node7(s38, s39)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3501, 3500])).
% 1.16/1.11 tff(3503,plain,
% 1.16/1.11 (node7(s38, s39)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3502, 206, 3499])).
% 1.16/1.11 tff(3504,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3505,plain,
% 1.16/1.11 (((~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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3506,plain,
% 1.16/1.11 (((~![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))))),
% 1.16/1.11 inference(monotonicity,[status(thm)],[3505])).
% 1.16/1.11 tff(3507,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(transitivity,[status(thm)],[3506, 3504])).
% 1.16/1.11 tff(3508,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3509,plain,
% 1.16/1.11 ((~![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))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3508, 3507])).
% 1.16/1.11 tff(3510,plain,
% 1.16/1.11 (m_main_v_state1(s39, c_n1) | (~m_main_v_state1(s38, c_c1)) | node1(s38) | node2(s38) | node3(s38) | node4(s38) | node5(s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3509, 584, 3503])).
% 1.16/1.11 tff(3511,plain,
% 1.16/1.11 (m_main_v_state1(s39, c_n1)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3510, 3492, 3432, 3484, 3480, 3472, 3455])).
% 1.16/1.11 tff(3512,plain,
% 1.16/1.11 (((~![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)))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3513,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s37, c_t2) | (~node15(s37)))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3514,plain,
% 1.16/1.11 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s37, c_t2) | (~node15(s37))),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3513, 3512])).
% 1.16/1.11 tff(3515,plain,
% 1.16/1.11 (~node15(s37)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3514, 103, 3409])).
% 1.16/1.11 tff(3516,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3517,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s37, s38)) | node18(s37, s38))),
% 1.16/1.11 inference(quant_inst,[status(thm)],[])).
% 1.16/1.11 tff(3518,plain,
% 1.16/1.11 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s37, s38)) | node18(s37, s38)),
% 1.16/1.11 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 1.16/1.11 tff(3519,plain,
% 1.16/1.11 (node18(s37, s38)),
% 1.16/1.11 inference(unit_resolution,[status(thm)],[3518, 125, 3420])).
% 1.16/1.11 tff(3520,plain,
% 1.16/1.11 (((~![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))),
% 1.16/1.11 inference(rewrite,[status(thm)],[])).
% 1.16/1.11 tff(3521,plain,
% 1.16/1.11 (((~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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3522,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(monotonicity,[status(thm)],[3521])).
% 1.16/1.12 tff(3523,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(transitivity,[status(thm)],[3522, 3520])).
% 1.16/1.12 tff(3524,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3525,plain,
% 1.16/1.12 ((~![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)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3524, 3523])).
% 1.16/1.12 tff(3526,plain,
% 1.16/1.12 (node15(s37) | (~m_main_v_state1(s37, c_t1)) | (~m_main_v_state2(s37, c_n2)) | m_main_v_turn(s38, c_1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3525, 992, 3519])).
% 1.16/1.12 tff(3527,plain,
% 1.16/1.12 (m_main_v_turn(s38, c_1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3526, 3515, 3337, 3405])).
% 1.16/1.12 tff(3528,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3529,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3530,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3529, 3528])).
% 1.16/1.12 tff(3531,plain,
% 1.16/1.12 (~m_main_v_turn(s38, c_2)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3530, 156, 3527])).
% 1.16/1.12 tff(3532,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3533,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s38, c_2) | (~node12(s38)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3534,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s38, c_2) | (~node12(s38))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 1.16/1.12 tff(3535,plain,
% 1.16/1.12 (~node12(s38)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3534, 184, 3531])).
% 1.16/1.12 tff(3536,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3537,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s38, c_n2) | (~node8(s38)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3538,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s38, c_n2) | (~node8(s38))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 1.16/1.12 tff(3539,plain,
% 1.16/1.12 (~node8(s38)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3538, 271, 3468])).
% 1.16/1.12 tff(3540,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3541,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s38, c_n2) | (~node9(s38)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3542,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s38, c_n2) | (~node9(s38))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 1.16/1.12 tff(3543,plain,
% 1.16/1.12 (~node9(s38)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3542, 88, 3468])).
% 1.16/1.12 tff(3544,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3545,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s38, c_n2) | (~node10(s38)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3546,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s38, c_n2) | (~node10(s38))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 1.16/1.12 tff(3547,plain,
% 1.16/1.12 (~node10(s38)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3546, 249, 3468])).
% 1.16/1.12 tff(3548,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3549,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s38, c_n1) | (~node11(s38)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3550,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s38, c_n1) | (~node11(s38))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3549, 3548])).
% 1.16/1.12 tff(3551,plain,
% 1.16/1.12 (~node11(s38)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3550, 238, 3488])).
% 1.16/1.12 tff(3552,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3553,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s38, s39)) | node14(s38, s39))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3554,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s38, s39)) | node14(s38, s39)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 1.16/1.12 tff(3555,plain,
% 1.16/1.12 (node14(s38, s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3554, 7, 3499])).
% 1.16/1.12 tff(3556,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3557,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3558,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 1.16/1.12 tff(3559,plain,
% 1.16/1.12 (m_main_v_state2(s38, c_c2) | node9(s38) | node8(s38) | node10(s38) | node11(s38) | node12(s38) | node13(s38, s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3558, 296, 3555])).
% 1.16/1.12 tff(3560,plain,
% 1.16/1.12 (node13(s38, s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3559, 3551, 3476, 3547, 3543, 3539, 3535])).
% 1.16/1.12 tff(3561,plain,
% 1.16/1.12 (((~![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(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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3562,plain,
% 1.16/1.12 (((~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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3563,plain,
% 1.16/1.12 (((~![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))))),
% 1.16/1.12 inference(monotonicity,[status(thm)],[3562])).
% 1.16/1.12 tff(3564,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.16/1.12 tff(3565,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3566,plain,
% 1.16/1.12 ((~![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(s38, c_t2)) | m_main_v_state2(s39, c_t2) | (~node13(s38, s39))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.16/1.12 tff(3567,plain,
% 1.16/1.12 (m_main_v_state2(s39, c_t2)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3566, 518, 3464, 3560])).
% 1.16/1.12 tff(3568,plain,
% 1.16/1.12 (succ(s39, s40) <=> succ(s39, s40)),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3569,axiom,(succ(s39, s40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound40')).
% 1.16/1.12 tff(3570,plain,
% 1.16/1.12 (succ(s39, s40)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3569, 3568])).
% 1.16/1.12 tff(3571,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3572,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3573,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3572, 3571])).
% 1.16/1.12 tff(3574,plain,
% 1.16/1.12 (trans(s39, s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3573, 3570, 39])).
% 1.16/1.12 tff(3575,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3576,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s39, s40)) | node7(s39, s40))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3577,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s39, s40)) | node7(s39, s40)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 1.16/1.12 tff(3578,plain,
% 1.16/1.12 (node7(s39, s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3577, 206, 3574])).
% 1.16/1.12 tff(3579,plain,
% 1.16/1.12 (((~![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(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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3580,plain,
% 1.16/1.12 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3581,plain,
% 1.16/1.12 ((~![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(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | (~node7(s39, s40)) | m_main_v_state1(s40, c_t1)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.16/1.12 tff(3582,plain,
% 1.16/1.12 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_state1(s40, c_t1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3581, 651, 3578])).
% 1.16/1.12 tff(3583,plain,
% 1.16/1.12 (m_main_v_state1(s40, c_t1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3582, 3567, 3511])).
% 1.16/1.12 tff(3584,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3585,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3586,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 1.16/1.12 tff(3587,plain,
% 1.16/1.12 (~m_main_v_state1(s40, c_n1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3586, 17, 3583])).
% 1.16/1.12 tff(3588,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3589,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s40, c_n1) | (~node1(s40)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3590,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s40, c_n1) | (~node1(s40))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.16/1.12 tff(3591,plain,
% 1.16/1.12 (~node1(s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3590, 421, 3587])).
% 1.16/1.12 tff(3592,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3593,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s39, s40)) | node18(s39, s40))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3594,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s39, s40)) | node18(s39, s40)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 1.16/1.12 tff(3595,plain,
% 1.16/1.12 (node18(s39, s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3594, 125, 3574])).
% 1.16/1.12 tff(3596,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3597,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3598,plain,
% 1.16/1.12 ((~![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)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3597, 3596])).
% 1.16/1.12 tff(3599,plain,
% 1.16/1.12 ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state2(s39, c_t2)) | m_main_v_turn(s40, c_2)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3598, 760, 3595])).
% 1.16/1.12 tff(3600,plain,
% 1.16/1.12 (m_main_v_turn(s40, c_2)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3599, 3567, 3511])).
% 1.16/1.12 tff(3601,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3602,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3603,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 1.16/1.12 tff(3604,plain,
% 1.16/1.12 (~m_main_v_turn(s40, c_1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3603, 156, 3600])).
% 1.16/1.12 tff(3605,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3606,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s40, c_1) | (~node5(s40)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3607,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s40, c_1) | (~node5(s40))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 1.16/1.12 tff(3608,plain,
% 1.16/1.12 (~node5(s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3607, 776, 3604])).
% 1.16/1.12 tff(3609,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3610,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s40, c_n1) | (~node2(s40)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3611,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s40, c_n1) | (~node2(s40))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 1.16/1.12 tff(3612,plain,
% 1.16/1.12 (~node2(s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3611, 787, 3587])).
% 1.16/1.12 tff(3613,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3614,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s40, c_n1) | (~node3(s40)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3615,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s40, c_n1) | (~node3(s40))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 1.16/1.12 tff(3616,plain,
% 1.16/1.12 (~node3(s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3615, 798, 3587])).
% 1.16/1.12 tff(3617,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3618,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3619,plain,
% 1.16/1.12 ((~![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))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3618, 3617])).
% 1.16/1.12 tff(3620,plain,
% 1.16/1.12 (~m_main_v_state1(s40, c_c1)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3619, 539, 3583])).
% 1.16/1.12 tff(3621,plain,
% 1.16/1.12 (((~![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(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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3622,plain,
% 1.16/1.12 (((~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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3623,plain,
% 1.16/1.12 (((~![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))))),
% 1.16/1.12 inference(monotonicity,[status(thm)],[3622])).
% 1.16/1.12 tff(3624,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(transitivity,[status(thm)],[3623, 3621])).
% 1.16/1.12 tff(3625,plain,
% 1.16/1.12 ((~![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)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3626,plain,
% 1.16/1.12 ((~![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(s38, c_n2) | (~m_main_v_state2(s39, c_n2)) | (~node13(s38, s39))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 1.16/1.12 tff(3627,plain,
% 1.16/1.12 (~m_main_v_state2(s39, c_n2)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3626, 311, 3468, 3560])).
% 1.16/1.12 tff(3628,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3629,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s39, c_n2) | (~node9(s39)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3630,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s39, c_n2) | (~node9(s39))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 1.16/1.12 tff(3631,plain,
% 1.16/1.12 (~node9(s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3630, 88, 3627])).
% 1.16/1.12 tff(3632,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3633,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s39, c_n2) | (~node10(s39)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3634,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s39, c_n2) | (~node10(s39))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 1.16/1.12 tff(3635,plain,
% 1.16/1.12 (~node10(s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3634, 249, 3627])).
% 1.16/1.12 tff(3636,plain,
% 1.16/1.12 (((~![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)))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3637,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s39, c_n2) | (~node8(s39)))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3638,plain,
% 1.16/1.12 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s39, c_n2) | (~node8(s39))),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 1.16/1.12 tff(3639,plain,
% 1.16/1.12 (~node8(s39)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3638, 271, 3627])).
% 1.16/1.12 tff(3640,plain,
% 1.16/1.12 (((~![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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3641,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s39, s40)) | node14(s39, s40))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3642,plain,
% 1.16/1.12 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s39, s40)) | node14(s39, s40)),
% 1.16/1.12 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 1.16/1.12 tff(3643,plain,
% 1.16/1.12 (node14(s39, s40)),
% 1.16/1.12 inference(unit_resolution,[status(thm)],[3642, 7, 3574])).
% 1.16/1.12 tff(3644,plain,
% 1.16/1.12 (((~![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(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))),
% 1.16/1.12 inference(rewrite,[status(thm)],[])).
% 1.16/1.12 tff(3645,plain,
% 1.16/1.12 ((~![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(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))),
% 1.16/1.12 inference(quant_inst,[status(thm)],[])).
% 1.16/1.12 tff(3646,plain,
% 1.16/1.12 ((~![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(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)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 1.16/1.13 tff(3647,plain,
% 1.16/1.13 ((~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)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3646, 617, 3643])).
% 1.16/1.13 tff(3648,plain,
% 1.16/1.13 (m_main_v_state2(s40, c_c2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3647, 3639, 3511, 3567, 3635, 3631])).
% 1.16/1.13 tff(3649,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3650,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3651,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 1.16/1.13 tff(3652,plain,
% 1.16/1.13 (~m_main_v_state2(s40, c_n2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3651, 697, 3648])).
% 1.16/1.13 tff(3653,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3654,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s40, c_n2) | (~node4(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3655,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s40, c_n2) | (~node4(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3654, 3653])).
% 1.16/1.13 tff(3656,plain,
% 1.16/1.13 (~node4(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3655, 388, 3652])).
% 1.16/1.13 tff(3657,plain,
% 1.16/1.13 (succ(s40, s41) <=> succ(s40, s41)),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3658,axiom,(succ(s40, s41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound41')).
% 1.16/1.13 tff(3659,plain,
% 1.16/1.13 (succ(s40, s41)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3658, 3657])).
% 1.16/1.13 tff(3660,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3661,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3662,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3661, 3660])).
% 1.16/1.13 tff(3663,plain,
% 1.16/1.13 (trans(s40, s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3662, 3659, 39])).
% 1.16/1.13 tff(3664,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3665,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s40, s41)) | node7(s40, s41))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3666,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s40, s41)) | node7(s40, s41)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 1.16/1.13 tff(3667,plain,
% 1.16/1.13 (node7(s40, s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3666, 206, 3663])).
% 1.16/1.13 tff(3668,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3669,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3670,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 1.16/1.13 tff(3671,plain,
% 1.16/1.13 (m_main_v_state1(s40, c_c1) | node1(s40) | node2(s40) | node3(s40) | node4(s40) | node5(s40) | node6(s40, s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3670, 820, 3667])).
% 1.16/1.13 tff(3672,plain,
% 1.16/1.13 (node6(s40, s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3671, 3656, 3620, 3616, 3612, 3608, 3591])).
% 1.16/1.13 tff(3673,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3674,plain,
% 1.16/1.13 (((~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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3675,plain,
% 1.16/1.13 (((~![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))))),
% 1.16/1.13 inference(monotonicity,[status(thm)],[3674])).
% 1.16/1.13 tff(3676,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(transitivity,[status(thm)],[3675, 3673])).
% 1.16/1.13 tff(3677,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3678,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3677, 3676])).
% 1.16/1.13 tff(3679,plain,
% 1.16/1.13 (m_main_v_state1(s41, c_t1)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3678, 856, 3583, 3672])).
% 1.16/1.13 tff(3680,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3681,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3682,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3681, 3680])).
% 1.16/1.13 tff(3683,plain,
% 1.16/1.13 (~m_main_v_state2(s40, c_t2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3682, 260, 3648])).
% 1.16/1.13 tff(3684,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3685,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s40, c_t2) | (~node12(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3686,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s40, c_t2) | (~node12(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 1.16/1.13 tff(3687,plain,
% 1.16/1.13 (~node12(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3686, 633, 3683])).
% 1.16/1.13 tff(3688,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3689,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s40, c_n1) | (~node11(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3690,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s40, c_n1) | (~node11(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 1.16/1.13 tff(3691,plain,
% 1.16/1.13 (~node11(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3690, 238, 3587])).
% 1.16/1.13 tff(3692,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3693,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s40, c_c1) | (~node10(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3694,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s40, c_c1) | (~node10(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 1.16/1.13 tff(3695,plain,
% 1.16/1.13 (~node10(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3694, 675, 3620])).
% 1.16/1.13 tff(3696,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3697,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s40, c_n1) | (~node9(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3698,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s40, c_n1) | (~node9(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.16/1.13 tff(3699,plain,
% 1.16/1.13 (~node9(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3698, 686, 3587])).
% 1.16/1.13 tff(3700,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3701,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s40, c_n2) | (~node8(s40)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3702,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s40, c_n2) | (~node8(s40))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3701, 3700])).
% 1.16/1.13 tff(3703,plain,
% 1.16/1.13 (~node8(s40)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3702, 271, 3652])).
% 1.16/1.13 tff(3704,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3705,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s40, s41)) | node14(s40, s41))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3706,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s40, s41)) | node14(s40, s41)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 1.16/1.13 tff(3707,plain,
% 1.16/1.13 (node14(s40, s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3706, 7, 3663])).
% 1.16/1.13 tff(3708,plain,
% 1.16/1.13 (((~![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(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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3709,plain,
% 1.16/1.13 (((~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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3710,plain,
% 1.16/1.13 (((~![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(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))))),
% 1.16/1.13 inference(monotonicity,[status(thm)],[3709])).
% 1.16/1.13 tff(3711,plain,
% 1.16/1.13 (((~![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(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)))),
% 1.16/1.13 inference(transitivity,[status(thm)],[3710, 3708])).
% 1.16/1.13 tff(3712,plain,
% 1.16/1.13 ((~![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(s40, c_c2)) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | m_main_v_state2(s41, c_n2))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3713,plain,
% 1.16/1.13 ((~![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(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~node14(s40, s41)) | (~m_main_v_state2(s40, c_c2))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3712, 3711])).
% 1.16/1.13 tff(3714,plain,
% 1.16/1.13 (m_main_v_state2(s41, c_n2) | node9(s40) | node8(s40) | node10(s40) | node11(s40) | node12(s40) | (~m_main_v_state2(s40, c_c2))),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3713, 726, 3707])).
% 1.16/1.13 tff(3715,plain,
% 1.16/1.13 (m_main_v_state2(s41, c_n2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3714, 3703, 3648, 3699, 3695, 3691, 3687])).
% 1.16/1.13 tff(3716,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3717,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3718,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 1.16/1.13 tff(3719,plain,
% 1.16/1.13 (~m_main_v_state2(s41, c_t2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3718, 77, 3715])).
% 1.16/1.13 tff(3720,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3721,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s41, c_t2) | (~node15(s41)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3722,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s41, c_t2) | (~node15(s41))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3721, 3720])).
% 1.16/1.13 tff(3723,plain,
% 1.16/1.13 (~node15(s41)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3722, 103, 3719])).
% 1.16/1.13 tff(3724,plain,
% 1.16/1.13 (succ(s41, s42) <=> succ(s41, s42)),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3725,axiom,(succ(s41, s42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound42')).
% 1.16/1.13 tff(3726,plain,
% 1.16/1.13 (succ(s41, s42)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 1.16/1.13 tff(3727,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3728,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3729,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 1.16/1.13 tff(3730,plain,
% 1.16/1.13 (trans(s41, s42)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3729, 3726, 39])).
% 1.16/1.13 tff(3731,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3732,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s41, s42)) | node18(s41, s42))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3733,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s41, s42)) | node18(s41, s42)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.16/1.13 tff(3734,plain,
% 1.16/1.13 (node18(s41, s42)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3733, 125, 3730])).
% 1.16/1.13 tff(3735,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3736,plain,
% 1.16/1.13 (((~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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3737,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(monotonicity,[status(thm)],[3736])).
% 1.16/1.13 tff(3738,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(transitivity,[status(thm)],[3737, 3735])).
% 1.16/1.13 tff(3739,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3740,plain,
% 1.16/1.13 ((~![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)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3739, 3738])).
% 1.16/1.13 tff(3741,plain,
% 1.16/1.13 (node15(s41) | (~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_turn(s42, c_1)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3740, 992, 3734])).
% 1.16/1.13 tff(3742,plain,
% 1.16/1.13 (m_main_v_turn(s42, c_1)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3741, 3723, 3715, 3679])).
% 1.16/1.13 tff(3743,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3744,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3745,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 1.16/1.13 tff(3746,plain,
% 1.16/1.13 (~m_main_v_turn(s42, c_2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3745, 156, 3742])).
% 1.16/1.13 tff(3747,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3748,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s42, c_2) | (~node12(s42)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3749,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s42, c_2) | (~node12(s42))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.16/1.13 tff(3750,plain,
% 1.16/1.13 (~node12(s42)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3749, 184, 3746])).
% 1.16/1.13 tff(3751,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3752,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s41, s42)) | node14(s41, s42))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3753,plain,
% 1.16/1.13 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s41, s42)) | node14(s41, s42)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3752, 3751])).
% 1.16/1.13 tff(3754,plain,
% 1.16/1.13 (node14(s41, s42)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3753, 7, 3730])).
% 1.16/1.13 tff(3755,plain,
% 1.16/1.13 (((~![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))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3756,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3757,plain,
% 1.16/1.13 ((~![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)),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 1.16/1.13 tff(3758,plain,
% 1.16/1.13 ((~m_main_v_state1(s41, c_t1)) | (~m_main_v_state2(s41, c_n2)) | m_main_v_state2(s42, c_t2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3757, 922, 3754])).
% 1.16/1.13 tff(3759,plain,
% 1.16/1.13 (m_main_v_state2(s42, c_t2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3758, 3679, 3715])).
% 1.16/1.13 tff(3760,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3761,plain,
% 1.16/1.13 ((~![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)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3762,plain,
% 1.16/1.13 ((~![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))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.16/1.13 tff(3763,plain,
% 1.16/1.13 (~m_main_v_state2(s42, c_n2)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3762, 77, 3759])).
% 1.16/1.13 tff(3764,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3765,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s42, c_n2) | (~node8(s42)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3766,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s42, c_n2) | (~node8(s42))),
% 1.16/1.13 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 1.16/1.13 tff(3767,plain,
% 1.16/1.13 (~node8(s42)),
% 1.16/1.13 inference(unit_resolution,[status(thm)],[3766, 271, 3763])).
% 1.16/1.13 tff(3768,plain,
% 1.16/1.13 (((~![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)))),
% 1.16/1.13 inference(rewrite,[status(thm)],[])).
% 1.16/1.13 tff(3769,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s42, c_n2) | (~node9(s42)))),
% 1.16/1.13 inference(quant_inst,[status(thm)],[])).
% 1.16/1.13 tff(3770,plain,
% 1.16/1.13 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s42, c_n2) | (~node9(s42))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3769, 3768])).
% 1.16/1.14 tff(3771,plain,
% 1.16/1.14 (~node9(s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3770, 88, 3763])).
% 1.16/1.14 tff(3772,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3773,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s42, c_n2) | (~node10(s42)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3774,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s42, c_n2) | (~node10(s42))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 1.16/1.14 tff(3775,plain,
% 1.16/1.14 (~node10(s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3774, 249, 3763])).
% 1.16/1.14 tff(3776,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3777,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3778,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 1.16/1.14 tff(3779,plain,
% 1.16/1.14 (~m_main_v_state2(s42, c_c2)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3778, 260, 3759])).
% 1.16/1.14 tff(3780,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3781,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3782,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 1.16/1.14 tff(3783,plain,
% 1.16/1.14 (~m_main_v_state2(s41, c_c2)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3782, 697, 3715])).
% 1.16/1.14 tff(3784,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3785,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s41, c_c2) | (~node3(s41)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3786,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s41, c_c2) | (~node3(s41))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3785, 3784])).
% 1.16/1.14 tff(3787,plain,
% 1.16/1.14 (~node3(s41)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3786, 399, 3783])).
% 1.16/1.14 tff(3788,plain,
% 1.16/1.14 (((~![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(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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3789,plain,
% 1.16/1.14 (((~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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3790,plain,
% 1.16/1.14 (((~![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))))),
% 1.16/1.14 inference(monotonicity,[status(thm)],[3789])).
% 1.16/1.14 tff(3791,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(transitivity,[status(thm)],[3790, 3788])).
% 1.16/1.14 tff(3792,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3793,plain,
% 1.16/1.14 ((~![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(s40, c_n1) | (~m_main_v_state1(s41, c_n1)) | (~node6(s40, s41))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 1.16/1.14 tff(3794,plain,
% 1.16/1.14 (~m_main_v_state1(s41, c_n1)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3793, 835, 3587, 3672])).
% 1.16/1.14 tff(3795,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3796,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s41, c_n1) | (~node2(s41)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3797,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s41, c_n1) | (~node2(s41))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 1.16/1.14 tff(3798,plain,
% 1.16/1.14 (~node2(s41)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3797, 787, 3794])).
% 1.16/1.14 tff(3799,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3800,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s41, c_t2) | (~node1(s41)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3801,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s41, c_t2) | (~node1(s41))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3800, 3799])).
% 1.16/1.14 tff(3802,plain,
% 1.16/1.14 (~node1(s41)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3801, 195, 3719])).
% 1.16/1.14 tff(3803,plain,
% 1.16/1.14 (((~![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))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3804,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s41, s42)) | node7(s41, s42))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3805,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s41, s42)) | node7(s41, s42)),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 1.16/1.14 tff(3806,plain,
% 1.16/1.14 (node7(s41, s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3805, 206, 3730])).
% 1.16/1.14 tff(3807,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3808,plain,
% 1.16/1.14 (((~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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3809,plain,
% 1.16/1.14 (((~![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))))),
% 1.16/1.14 inference(monotonicity,[status(thm)],[3808])).
% 1.16/1.14 tff(3810,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(transitivity,[status(thm)],[3809, 3807])).
% 1.16/1.14 tff(3811,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3812,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3811, 3810])).
% 1.16/1.14 tff(3813,plain,
% 1.16/1.14 ((~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)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3812, 892, 3806])).
% 1.16/1.14 tff(3814,plain,
% 1.16/1.14 (m_main_v_state1(s42, c_c1)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3813, 3802, 3715, 3679, 3798, 3787])).
% 1.16/1.14 tff(3815,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3816,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3817,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 1.16/1.14 tff(3818,plain,
% 1.16/1.14 (~m_main_v_state1(s42, c_n1)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3817, 454, 3814])).
% 1.16/1.14 tff(3819,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3820,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s42, c_n1) | (~node11(s42)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3821,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s42, c_n1) | (~node11(s42))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.16/1.14 tff(3822,plain,
% 1.16/1.14 (~node11(s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3821, 238, 3818])).
% 1.16/1.14 tff(3823,plain,
% 1.16/1.14 (succ(s42, s43) <=> succ(s42, s43)),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3824,axiom,(succ(s42, s43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound43')).
% 1.16/1.14 tff(3825,plain,
% 1.16/1.14 (succ(s42, s43)),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 1.16/1.14 tff(3826,plain,
% 1.16/1.14 (((~![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))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3827,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3828,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 1.16/1.14 tff(3829,plain,
% 1.16/1.14 (trans(s42, s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3828, 3825, 39])).
% 1.16/1.14 tff(3830,plain,
% 1.16/1.14 (((~![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))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3831,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s42, s43)) | node14(s42, s43))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3832,plain,
% 1.16/1.14 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s42, s43)) | node14(s42, s43)),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3831, 3830])).
% 1.16/1.14 tff(3833,plain,
% 1.16/1.14 (node14(s42, s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3832, 7, 3829])).
% 1.16/1.14 tff(3834,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3835,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3836,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 1.16/1.14 tff(3837,plain,
% 1.16/1.14 (m_main_v_state2(s42, c_c2) | node9(s42) | node8(s42) | node10(s42) | node11(s42) | node12(s42) | node13(s42, s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3836, 296, 3833])).
% 1.16/1.14 tff(3838,plain,
% 1.16/1.14 (node13(s42, s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3837, 3822, 3779, 3775, 3771, 3767, 3750])).
% 1.16/1.14 tff(3839,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3840,plain,
% 1.16/1.14 (((~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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3841,plain,
% 1.16/1.14 (((~![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))))),
% 1.16/1.14 inference(monotonicity,[status(thm)],[3840])).
% 1.16/1.14 tff(3842,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(transitivity,[status(thm)],[3841, 3839])).
% 1.16/1.14 tff(3843,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3844,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 1.16/1.14 tff(3845,plain,
% 1.16/1.14 (~m_main_v_state2(s43, c_n2)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3844, 311, 3763, 3838])).
% 1.16/1.14 tff(3846,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3847,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s43, c_n2) | (~node9(s43)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3848,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s43, c_n2) | (~node9(s43))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 1.16/1.14 tff(3849,plain,
% 1.16/1.14 (~node9(s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3848, 88, 3845])).
% 1.16/1.14 tff(3850,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3851,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s43, c_n2) | (~node10(s43)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3852,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s43, c_n2) | (~node10(s43))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3851, 3850])).
% 1.16/1.14 tff(3853,plain,
% 1.16/1.14 (~node10(s43)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3852, 249, 3845])).
% 1.16/1.14 tff(3854,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3855,plain,
% 1.16/1.14 (((~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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3856,plain,
% 1.16/1.14 (((~![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))))),
% 1.16/1.14 inference(monotonicity,[status(thm)],[3855])).
% 1.16/1.14 tff(3857,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(transitivity,[status(thm)],[3856, 3854])).
% 1.16/1.14 tff(3858,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3859,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3858, 3857])).
% 1.16/1.14 tff(3860,plain,
% 1.16/1.14 (m_main_v_state2(s43, c_t2)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3859, 518, 3759, 3838])).
% 1.16/1.14 tff(3861,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3862,plain,
% 1.16/1.14 ((~![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)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3863,plain,
% 1.16/1.14 ((~![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))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 1.16/1.14 tff(3864,plain,
% 1.16/1.14 (~m_main_v_state1(s42, c_t1)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3863, 539, 3814])).
% 1.16/1.14 tff(3865,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3866,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s42, c_t1) | (~node5(s42)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3867,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s42, c_t1) | (~node5(s42))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3866, 3865])).
% 1.16/1.14 tff(3868,plain,
% 1.16/1.14 (~node5(s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3867, 550, 3864])).
% 1.16/1.14 tff(3869,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.14 inference(rewrite,[status(thm)],[])).
% 1.16/1.14 tff(3870,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s42, c_n2) | (~node4(s42)))),
% 1.16/1.14 inference(quant_inst,[status(thm)],[])).
% 1.16/1.14 tff(3871,plain,
% 1.16/1.14 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s42, c_n2) | (~node4(s42))),
% 1.16/1.14 inference(modus_ponens,[status(thm)],[3870, 3869])).
% 1.16/1.14 tff(3872,plain,
% 1.16/1.14 (~node4(s42)),
% 1.16/1.14 inference(unit_resolution,[status(thm)],[3871, 388, 3763])).
% 1.16/1.14 tff(3873,plain,
% 1.16/1.14 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3874,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s42, c_c2) | (~node3(s42)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3875,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s42, c_c2) | (~node3(s42))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 1.16/1.15 tff(3876,plain,
% 1.16/1.15 (~node3(s42)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3875, 399, 3779])).
% 1.16/1.15 tff(3877,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3878,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s42, c_n2) | (~node2(s42)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3879,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s42, c_n2) | (~node2(s42))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3878, 3877])).
% 1.16/1.15 tff(3880,plain,
% 1.16/1.15 (~node2(s42)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3879, 410, 3763])).
% 1.16/1.15 tff(3881,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3882,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s42, c_n1) | (~node1(s42)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3883,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s42, c_n1) | (~node1(s42))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 1.16/1.15 tff(3884,plain,
% 1.16/1.15 (~node1(s42)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3883, 421, 3818])).
% 1.16/1.15 tff(3885,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3886,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s42, s43)) | node7(s42, s43))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3887,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s42, s43)) | node7(s42, s43)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3886, 3885])).
% 1.16/1.15 tff(3888,plain,
% 1.16/1.15 (node7(s42, s43)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3887, 206, 3829])).
% 1.16/1.15 tff(3889,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3890,plain,
% 1.16/1.15 (((~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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3891,plain,
% 1.16/1.15 (((~![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))))),
% 1.16/1.15 inference(monotonicity,[status(thm)],[3890])).
% 1.16/1.15 tff(3892,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(transitivity,[status(thm)],[3891, 3889])).
% 1.16/1.15 tff(3893,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3894,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 1.16/1.15 tff(3895,plain,
% 1.16/1.15 (m_main_v_state1(s43, c_n1) | (~m_main_v_state1(s42, c_c1)) | node1(s42) | node2(s42) | node3(s42) | node4(s42) | node5(s42)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3894, 584, 3888])).
% 1.16/1.15 tff(3896,plain,
% 1.16/1.15 (m_main_v_state1(s43, c_n1)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3895, 3884, 3814, 3880, 3876, 3872, 3868])).
% 1.16/1.15 tff(3897,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3898,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s43, c_n2) | (~node8(s43)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3899,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s43, c_n2) | (~node8(s43))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 1.16/1.15 tff(3900,plain,
% 1.16/1.15 (~node8(s43)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3899, 271, 3845])).
% 1.16/1.15 tff(3901,plain,
% 1.16/1.15 (succ(s43, s44) <=> succ(s43, s44)),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3902,axiom,(succ(s43, s44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound44')).
% 1.16/1.15 tff(3903,plain,
% 1.16/1.15 (succ(s43, s44)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 1.16/1.15 tff(3904,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3905,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3906,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 1.16/1.15 tff(3907,plain,
% 1.16/1.15 (trans(s43, s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3906, 3903, 39])).
% 1.16/1.15 tff(3908,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3909,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s43, s44)) | node14(s43, s44))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3910,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s43, s44)) | node14(s43, s44)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3909, 3908])).
% 1.16/1.15 tff(3911,plain,
% 1.16/1.15 (node14(s43, s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3910, 7, 3907])).
% 1.16/1.15 tff(3912,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3913,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3914,plain,
% 1.16/1.15 ((~![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)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3913, 3912])).
% 1.16/1.15 tff(3915,plain,
% 1.16/1.15 ((~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)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3914, 617, 3911])).
% 1.16/1.15 tff(3916,plain,
% 1.16/1.15 (m_main_v_state2(s44, c_c2)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3915, 3900, 3896, 3860, 3853, 3849])).
% 1.16/1.15 tff(3917,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3918,plain,
% 1.16/1.15 ((~![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)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3919,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3918, 3917])).
% 1.16/1.15 tff(3920,plain,
% 1.16/1.15 (~m_main_v_state2(s44, c_t2)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3919, 260, 3916])).
% 1.16/1.15 tff(3921,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3922,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s44, c_t2) | (~node12(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3923,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s44, c_t2) | (~node12(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.16/1.15 tff(3924,plain,
% 1.16/1.15 (~node12(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3923, 633, 3920])).
% 1.16/1.15 tff(3925,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3926,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s43, s44)) | node7(s43, s44))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3927,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s43, s44)) | node7(s43, s44)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3926, 3925])).
% 1.16/1.15 tff(3928,plain,
% 1.16/1.15 (node7(s43, s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3927, 206, 3907])).
% 1.16/1.15 tff(3929,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3930,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3931,plain,
% 1.16/1.15 ((~![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)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 1.16/1.15 tff(3932,plain,
% 1.16/1.15 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_state1(s44, c_t1)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3931, 651, 3928])).
% 1.16/1.15 tff(3933,plain,
% 1.16/1.15 (m_main_v_state1(s44, c_t1)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3932, 3860, 3896])).
% 1.16/1.15 tff(3934,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3935,plain,
% 1.16/1.15 ((~![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)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3936,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3935, 3934])).
% 1.16/1.15 tff(3937,plain,
% 1.16/1.15 (~m_main_v_state1(s44, c_n1)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3936, 17, 3933])).
% 1.16/1.15 tff(3938,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3939,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s44, c_n1) | (~node11(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3940,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s44, c_n1) | (~node11(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3939, 3938])).
% 1.16/1.15 tff(3941,plain,
% 1.16/1.15 (~node11(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3940, 238, 3937])).
% 1.16/1.15 tff(3942,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3943,plain,
% 1.16/1.15 ((~![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)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3944,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.16/1.15 tff(3945,plain,
% 1.16/1.15 (~m_main_v_state1(s44, c_c1)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3944, 539, 3933])).
% 1.16/1.15 tff(3946,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3947,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s44, c_c1) | (~node10(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3948,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s44, c_c1) | (~node10(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3947, 3946])).
% 1.16/1.15 tff(3949,plain,
% 1.16/1.15 (~node10(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3948, 675, 3945])).
% 1.16/1.15 tff(3950,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3951,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s44, c_n1) | (~node9(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3952,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s44, c_n1) | (~node9(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 1.16/1.15 tff(3953,plain,
% 1.16/1.15 (~node9(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3952, 686, 3937])).
% 1.16/1.15 tff(3954,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3955,plain,
% 1.16/1.15 ((~![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)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3956,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 1.16/1.15 tff(3957,plain,
% 1.16/1.15 (~m_main_v_state2(s44, c_n2)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3956, 697, 3916])).
% 1.16/1.15 tff(3958,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3959,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s44, c_n2) | (~node8(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3960,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s44, c_n2) | (~node8(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3959, 3958])).
% 1.16/1.15 tff(3961,plain,
% 1.16/1.15 (~node8(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3960, 271, 3957])).
% 1.16/1.15 tff(3962,plain,
% 1.16/1.15 (succ(s44, s45) <=> succ(s44, s45)),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3963,axiom,(succ(s44, s45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound45')).
% 1.16/1.15 tff(3964,plain,
% 1.16/1.15 (succ(s44, s45)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 1.16/1.15 tff(3965,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3966,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3967,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3966, 3965])).
% 1.16/1.15 tff(3968,plain,
% 1.16/1.15 (trans(s44, s45)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3967, 3964, 39])).
% 1.16/1.15 tff(3969,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3970,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s44, s45)) | node14(s44, s45))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3971,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s44, s45)) | node14(s44, s45)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 1.16/1.15 tff(3972,plain,
% 1.16/1.15 (node14(s44, s45)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3971, 7, 3968])).
% 1.16/1.15 tff(3973,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3974,plain,
% 1.16/1.15 (((~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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3975,plain,
% 1.16/1.15 (((~![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))))),
% 1.16/1.15 inference(monotonicity,[status(thm)],[3974])).
% 1.16/1.15 tff(3976,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(transitivity,[status(thm)],[3975, 3973])).
% 1.16/1.15 tff(3977,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3978,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 1.16/1.15 tff(3979,plain,
% 1.16/1.15 (m_main_v_state2(s45, c_n2) | node9(s44) | node8(s44) | node10(s44) | node11(s44) | node12(s44) | (~m_main_v_state2(s44, c_c2))),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3978, 726, 3972])).
% 1.16/1.15 tff(3980,plain,
% 1.16/1.15 (m_main_v_state2(s45, c_n2)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3979, 3961, 3916, 3953, 3949, 3941, 3924])).
% 1.16/1.15 tff(3981,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3982,plain,
% 1.16/1.15 ((~![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)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3983,plain,
% 1.16/1.15 ((~![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))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 1.16/1.15 tff(3984,plain,
% 1.16/1.15 (~m_main_v_state2(s45, c_c2)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3983, 697, 3980])).
% 1.16/1.15 tff(3985,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3986,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s45, c_c2) | (~node3(s45)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3987,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s45, c_c2) | (~node3(s45))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 1.16/1.15 tff(3988,plain,
% 1.16/1.15 (~node3(s45)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3987, 399, 3984])).
% 1.16/1.15 tff(3989,plain,
% 1.16/1.15 (((~![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)))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3990,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s44, c_n1) | (~node1(s44)))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3991,plain,
% 1.16/1.15 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s44, c_n1) | (~node1(s44))),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3990, 3989])).
% 1.16/1.15 tff(3992,plain,
% 1.16/1.15 (~node1(s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3991, 421, 3937])).
% 1.16/1.15 tff(3993,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.15 inference(rewrite,[status(thm)],[])).
% 1.16/1.15 tff(3994,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s43, s44)) | node18(s43, s44))),
% 1.16/1.15 inference(quant_inst,[status(thm)],[])).
% 1.16/1.15 tff(3995,plain,
% 1.16/1.15 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s43, s44)) | node18(s43, s44)),
% 1.16/1.15 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 1.16/1.15 tff(3996,plain,
% 1.16/1.15 (node18(s43, s44)),
% 1.16/1.15 inference(unit_resolution,[status(thm)],[3995, 125, 3907])).
% 1.16/1.15 tff(3997,plain,
% 1.16/1.15 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(3998,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(3999,plain,
% 1.16/1.16 ((~![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)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.16/1.16 tff(4000,plain,
% 1.16/1.16 ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state2(s43, c_t2)) | m_main_v_turn(s44, c_2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[3999, 760, 3996])).
% 1.16/1.16 tff(4001,plain,
% 1.16/1.16 (m_main_v_turn(s44, c_2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4000, 3860, 3896])).
% 1.16/1.16 tff(4002,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4003,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4004,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4003, 4002])).
% 1.16/1.16 tff(4005,plain,
% 1.16/1.16 (~m_main_v_turn(s44, c_1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4004, 156, 4001])).
% 1.16/1.16 tff(4006,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4007,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s44, c_1) | (~node5(s44)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4008,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s44, c_1) | (~node5(s44))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4007, 4006])).
% 1.16/1.16 tff(4009,plain,
% 1.16/1.16 (~node5(s44)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4008, 776, 4005])).
% 1.16/1.16 tff(4010,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4011,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s44, c_n1) | (~node2(s44)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4012,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s44, c_n1) | (~node2(s44))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4011, 4010])).
% 1.16/1.16 tff(4013,plain,
% 1.16/1.16 (~node2(s44)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4012, 787, 3937])).
% 1.16/1.16 tff(4014,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4015,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s44, c_n1) | (~node3(s44)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4016,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s44, c_n1) | (~node3(s44))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 1.16/1.16 tff(4017,plain,
% 1.16/1.16 (~node3(s44)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4016, 798, 3937])).
% 1.16/1.16 tff(4018,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4019,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s44, c_n2) | (~node4(s44)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4020,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s44, c_n2) | (~node4(s44))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4019, 4018])).
% 1.16/1.16 tff(4021,plain,
% 1.16/1.16 (~node4(s44)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4020, 388, 3957])).
% 1.16/1.16 tff(4022,plain,
% 1.16/1.16 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4023,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s44, s45)) | node7(s44, s45))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4024,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s44, s45)) | node7(s44, s45)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4023, 4022])).
% 1.16/1.16 tff(4025,plain,
% 1.16/1.16 (node7(s44, s45)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4024, 206, 3968])).
% 1.16/1.16 tff(4026,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4027,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4028,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4027, 4026])).
% 1.16/1.16 tff(4029,plain,
% 1.16/1.16 (m_main_v_state1(s44, c_c1) | node1(s44) | node2(s44) | node3(s44) | node4(s44) | node5(s44) | node6(s44, s45)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4028, 820, 4025])).
% 1.16/1.16 tff(4030,plain,
% 1.16/1.16 (node6(s44, s45)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4029, 4021, 3945, 4017, 4013, 4009, 3992])).
% 1.16/1.16 tff(4031,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4032,plain,
% 1.16/1.16 (((~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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4033,plain,
% 1.16/1.16 (((~![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))))),
% 1.16/1.16 inference(monotonicity,[status(thm)],[4032])).
% 1.16/1.16 tff(4034,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(transitivity,[status(thm)],[4033, 4031])).
% 1.16/1.16 tff(4035,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4036,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 1.16/1.16 tff(4037,plain,
% 1.16/1.16 (~m_main_v_state1(s45, c_n1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4036, 835, 3937, 4030])).
% 1.16/1.16 tff(4038,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4039,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s45, c_n1) | (~node2(s45)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4040,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s45, c_n1) | (~node2(s45))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 1.16/1.16 tff(4041,plain,
% 1.16/1.16 (~node2(s45)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4040, 787, 4037])).
% 1.16/1.16 tff(4042,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4043,plain,
% 1.16/1.16 (((~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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4044,plain,
% 1.16/1.16 (((~![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))))),
% 1.16/1.16 inference(monotonicity,[status(thm)],[4043])).
% 1.16/1.16 tff(4045,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(transitivity,[status(thm)],[4044, 4042])).
% 1.16/1.16 tff(4046,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4047,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 1.16/1.16 tff(4048,plain,
% 1.16/1.16 (m_main_v_state1(s45, c_t1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4047, 856, 3933, 4030])).
% 1.16/1.16 tff(4049,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4050,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4051,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4050, 4049])).
% 1.16/1.16 tff(4052,plain,
% 1.16/1.16 (~m_main_v_state2(s45, c_t2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4051, 77, 3980])).
% 1.16/1.16 tff(4053,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4054,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s45, c_t2) | (~node1(s45)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4055,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s45, c_t2) | (~node1(s45))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 1.16/1.16 tff(4056,plain,
% 1.16/1.16 (~node1(s45)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4055, 195, 4052])).
% 1.16/1.16 tff(4057,plain,
% 1.16/1.16 (succ(s45, s46) <=> succ(s45, s46)),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4058,axiom,(succ(s45, s46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound46')).
% 1.16/1.16 tff(4059,plain,
% 1.16/1.16 (succ(s45, s46)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4058, 4057])).
% 1.16/1.16 tff(4060,plain,
% 1.16/1.16 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4061,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4062,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4061, 4060])).
% 1.16/1.16 tff(4063,plain,
% 1.16/1.16 (trans(s45, s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4062, 4059, 39])).
% 1.16/1.16 tff(4064,plain,
% 1.16/1.16 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4065,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s45, s46)) | node7(s45, s46))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4066,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s45, s46)) | node7(s45, s46)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.16/1.16 tff(4067,plain,
% 1.16/1.16 (node7(s45, s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4066, 206, 4063])).
% 1.16/1.16 tff(4068,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4069,plain,
% 1.16/1.16 (((~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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4070,plain,
% 1.16/1.16 (((~![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))))),
% 1.16/1.16 inference(monotonicity,[status(thm)],[4069])).
% 1.16/1.16 tff(4071,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(transitivity,[status(thm)],[4070, 4068])).
% 1.16/1.16 tff(4072,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4073,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4072, 4071])).
% 1.16/1.16 tff(4074,plain,
% 1.16/1.16 ((~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)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4073, 892, 4067])).
% 1.16/1.16 tff(4075,plain,
% 1.16/1.16 (m_main_v_state1(s46, c_c1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4074, 4056, 3980, 4048, 4041, 3988])).
% 1.16/1.16 tff(4076,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4077,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4078,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4077, 4076])).
% 1.16/1.16 tff(4079,plain,
% 1.16/1.16 (~m_main_v_state1(s46, c_t1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4078, 539, 4075])).
% 1.16/1.16 tff(4080,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4081,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s46, c_t1) | (~node5(s46)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4082,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s46, c_t1) | (~node5(s46))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4081, 4080])).
% 1.16/1.16 tff(4083,plain,
% 1.16/1.16 (~node5(s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4082, 550, 4079])).
% 1.16/1.16 tff(4084,plain,
% 1.16/1.16 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4085,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s45, s46)) | node14(s45, s46))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4086,plain,
% 1.16/1.16 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s45, s46)) | node14(s45, s46)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4085, 4084])).
% 1.16/1.16 tff(4087,plain,
% 1.16/1.16 (node14(s45, s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4086, 7, 4063])).
% 1.16/1.16 tff(4088,plain,
% 1.16/1.16 (((~![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))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4089,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4090,plain,
% 1.16/1.16 ((~![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)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 1.16/1.16 tff(4091,plain,
% 1.16/1.16 ((~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_state2(s46, c_t2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4090, 922, 4087])).
% 1.16/1.16 tff(4092,plain,
% 1.16/1.16 (m_main_v_state2(s46, c_t2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4091, 4048, 3980])).
% 1.16/1.16 tff(4093,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4094,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4095,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4094, 4093])).
% 1.16/1.16 tff(4096,plain,
% 1.16/1.16 (~m_main_v_state2(s46, c_n2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4095, 77, 4092])).
% 1.16/1.16 tff(4097,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4098,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s46, c_n2) | (~node4(s46)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4099,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s46, c_n2) | (~node4(s46))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4098, 4097])).
% 1.16/1.16 tff(4100,plain,
% 1.16/1.16 (~node4(s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4099, 388, 4096])).
% 1.16/1.16 tff(4101,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4102,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4103,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4102, 4101])).
% 1.16/1.16 tff(4104,plain,
% 1.16/1.16 (~m_main_v_state2(s46, c_c2)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4103, 260, 4092])).
% 1.16/1.16 tff(4105,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4106,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s46, c_c2) | (~node3(s46)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4107,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s46, c_c2) | (~node3(s46))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4106, 4105])).
% 1.16/1.16 tff(4108,plain,
% 1.16/1.16 (~node3(s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4107, 399, 4104])).
% 1.16/1.16 tff(4109,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4110,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s46, c_n2) | (~node2(s46)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4111,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s46, c_n2) | (~node2(s46))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 1.16/1.16 tff(4112,plain,
% 1.16/1.16 (~node2(s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4111, 410, 4096])).
% 1.16/1.16 tff(4113,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4114,plain,
% 1.16/1.16 ((~![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)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4115,plain,
% 1.16/1.16 ((~![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))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4114, 4113])).
% 1.16/1.16 tff(4116,plain,
% 1.16/1.16 (~m_main_v_state1(s46, c_n1)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4115, 454, 4075])).
% 1.16/1.16 tff(4117,plain,
% 1.16/1.16 (((~![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)))),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4118,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s46, c_n1) | (~node1(s46)))),
% 1.16/1.16 inference(quant_inst,[status(thm)],[])).
% 1.16/1.16 tff(4119,plain,
% 1.16/1.16 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s46, c_n1) | (~node1(s46))),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 1.16/1.16 tff(4120,plain,
% 1.16/1.16 (~node1(s46)),
% 1.16/1.16 inference(unit_resolution,[status(thm)],[4119, 421, 4116])).
% 1.16/1.16 tff(4121,plain,
% 1.16/1.16 (succ(s46, s47) <=> succ(s46, s47)),
% 1.16/1.16 inference(rewrite,[status(thm)],[])).
% 1.16/1.16 tff(4122,axiom,(succ(s46, s47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound47')).
% 1.16/1.16 tff(4123,plain,
% 1.16/1.16 (succ(s46, s47)),
% 1.16/1.16 inference(modus_ponens,[status(thm)],[4122, 4121])).
% 1.16/1.17 tff(4124,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4125,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4126,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4125, 4124])).
% 1.16/1.17 tff(4127,plain,
% 1.16/1.17 (trans(s46, s47)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4126, 4123, 39])).
% 1.16/1.17 tff(4128,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4129,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s46, s47)) | node7(s46, s47))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4130,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s46, s47)) | node7(s46, s47)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 1.16/1.17 tff(4131,plain,
% 1.16/1.17 (node7(s46, s47)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4130, 206, 4127])).
% 1.16/1.17 tff(4132,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4133,plain,
% 1.16/1.17 (((~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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4134,plain,
% 1.16/1.17 (((~![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))))),
% 1.16/1.17 inference(monotonicity,[status(thm)],[4133])).
% 1.16/1.17 tff(4135,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(transitivity,[status(thm)],[4134, 4132])).
% 1.16/1.17 tff(4136,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4137,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 1.16/1.17 tff(4138,plain,
% 1.16/1.17 (m_main_v_state1(s47, c_n1) | (~m_main_v_state1(s46, c_c1)) | node1(s46) | node2(s46) | node3(s46) | node4(s46) | node5(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4137, 584, 4131])).
% 1.16/1.17 tff(4139,plain,
% 1.16/1.17 (m_main_v_state1(s47, c_n1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4138, 4120, 4075, 4112, 4108, 4100, 4083])).
% 1.16/1.17 tff(4140,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4141,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s45, c_t2) | (~node15(s45)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4142,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s45, c_t2) | (~node15(s45))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 1.16/1.17 tff(4143,plain,
% 1.16/1.17 (~node15(s45)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4142, 103, 4052])).
% 1.16/1.17 tff(4144,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4145,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s45, s46)) | node18(s45, s46))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4146,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s45, s46)) | node18(s45, s46)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4145, 4144])).
% 1.16/1.17 tff(4147,plain,
% 1.16/1.17 (node18(s45, s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4146, 125, 4063])).
% 1.16/1.17 tff(4148,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4149,plain,
% 1.16/1.17 (((~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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4150,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(monotonicity,[status(thm)],[4149])).
% 1.16/1.17 tff(4151,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(transitivity,[status(thm)],[4150, 4148])).
% 1.16/1.17 tff(4152,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4153,plain,
% 1.16/1.17 ((~![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)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 1.16/1.17 tff(4154,plain,
% 1.16/1.17 (node15(s45) | (~m_main_v_state1(s45, c_t1)) | (~m_main_v_state2(s45, c_n2)) | m_main_v_turn(s46, c_1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4153, 992, 4147])).
% 1.16/1.17 tff(4155,plain,
% 1.16/1.17 (m_main_v_turn(s46, c_1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4154, 4143, 3980, 4048])).
% 1.16/1.17 tff(4156,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4157,plain,
% 1.16/1.17 ((~![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)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4158,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4157, 4156])).
% 1.16/1.17 tff(4159,plain,
% 1.16/1.17 (~m_main_v_turn(s46, c_2)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4158, 156, 4155])).
% 1.16/1.17 tff(4160,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4161,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s46, c_2) | (~node12(s46)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4162,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s46, c_2) | (~node12(s46))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 1.16/1.17 tff(4163,plain,
% 1.16/1.17 (~node12(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4162, 184, 4159])).
% 1.16/1.17 tff(4164,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4165,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s46, c_n2) | (~node8(s46)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4166,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s46, c_n2) | (~node8(s46))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4165, 4164])).
% 1.16/1.17 tff(4167,plain,
% 1.16/1.17 (~node8(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4166, 271, 4096])).
% 1.16/1.17 tff(4168,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4169,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s46, c_n2) | (~node9(s46)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4170,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s46, c_n2) | (~node9(s46))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 1.16/1.17 tff(4171,plain,
% 1.16/1.17 (~node9(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4170, 88, 4096])).
% 1.16/1.17 tff(4172,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4173,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s46, c_n2) | (~node10(s46)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4174,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s46, c_n2) | (~node10(s46))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.16/1.17 tff(4175,plain,
% 1.16/1.17 (~node10(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4174, 249, 4096])).
% 1.16/1.17 tff(4176,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4177,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s46, c_n1) | (~node11(s46)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4178,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s46, c_n1) | (~node11(s46))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 1.16/1.17 tff(4179,plain,
% 1.16/1.17 (~node11(s46)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4178, 238, 4116])).
% 1.16/1.17 tff(4180,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4181,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s46, s47)) | node14(s46, s47))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4182,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s46, s47)) | node14(s46, s47)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.16/1.17 tff(4183,plain,
% 1.16/1.17 (node14(s46, s47)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4182, 7, 4127])).
% 1.16/1.17 tff(4184,plain,
% 1.16/1.17 (((~![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(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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4185,plain,
% 1.16/1.17 ((~![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(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4186,plain,
% 1.16/1.17 ((~![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(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47) | (~node14(s46, s47))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 1.16/1.17 tff(4187,plain,
% 1.16/1.17 (m_main_v_state2(s46, c_c2) | node9(s46) | node8(s46) | node10(s46) | node11(s46) | node12(s46) | node13(s46, s47)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4186, 296, 4183])).
% 1.16/1.17 tff(4188,plain,
% 1.16/1.17 (node13(s46, s47)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4187, 4179, 4104, 4175, 4171, 4167, 4163])).
% 1.16/1.17 tff(4189,plain,
% 1.16/1.17 (((~![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(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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4190,plain,
% 1.16/1.17 (((~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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4191,plain,
% 1.16/1.17 (((~![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))))),
% 1.16/1.17 inference(monotonicity,[status(thm)],[4190])).
% 1.16/1.17 tff(4192,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(transitivity,[status(thm)],[4191, 4189])).
% 1.16/1.17 tff(4193,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4194,plain,
% 1.16/1.17 ((~![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(s46, c_t2)) | m_main_v_state2(s47, c_t2) | (~node13(s46, s47))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 1.16/1.17 tff(4195,plain,
% 1.16/1.17 (m_main_v_state2(s47, c_t2)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4194, 518, 4092, 4188])).
% 1.16/1.17 tff(4196,plain,
% 1.16/1.17 (succ(s47, s48) <=> succ(s47, s48)),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4197,axiom,(succ(s47, s48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound48')).
% 1.16/1.17 tff(4198,plain,
% 1.16/1.17 (succ(s47, s48)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4197, 4196])).
% 1.16/1.17 tff(4199,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4200,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4201,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4200, 4199])).
% 1.16/1.17 tff(4202,plain,
% 1.16/1.17 (trans(s47, s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4201, 4198, 39])).
% 1.16/1.17 tff(4203,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4204,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s47, s48)) | node7(s47, s48))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4205,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s47, s48)) | node7(s47, s48)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4204, 4203])).
% 1.16/1.17 tff(4206,plain,
% 1.16/1.17 (node7(s47, s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4205, 206, 4202])).
% 1.16/1.17 tff(4207,plain,
% 1.16/1.17 (((~![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(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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4208,plain,
% 1.16/1.17 ((~![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(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4209,plain,
% 1.16/1.17 ((~![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(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | (~node7(s47, s48)) | m_main_v_state1(s48, c_t1)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 1.16/1.17 tff(4210,plain,
% 1.16/1.17 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_state1(s48, c_t1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4209, 651, 4206])).
% 1.16/1.17 tff(4211,plain,
% 1.16/1.17 (m_main_v_state1(s48, c_t1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4210, 4195, 4139])).
% 1.16/1.17 tff(4212,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4213,plain,
% 1.16/1.17 ((~![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)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4214,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4213, 4212])).
% 1.16/1.17 tff(4215,plain,
% 1.16/1.17 (~m_main_v_state1(s48, c_n1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4214, 17, 4211])).
% 1.16/1.17 tff(4216,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4217,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s48, c_n1) | (~node1(s48)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4218,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s48, c_n1) | (~node1(s48))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 1.16/1.17 tff(4219,plain,
% 1.16/1.17 (~node1(s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4218, 421, 4215])).
% 1.16/1.17 tff(4220,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4221,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s47, s48)) | node18(s47, s48))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4222,plain,
% 1.16/1.17 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s47, s48)) | node18(s47, s48)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 1.16/1.17 tff(4223,plain,
% 1.16/1.17 (node18(s47, s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4222, 125, 4202])).
% 1.16/1.17 tff(4224,plain,
% 1.16/1.17 (((~![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))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4225,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4226,plain,
% 1.16/1.17 ((~![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)),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 1.16/1.17 tff(4227,plain,
% 1.16/1.17 ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state2(s47, c_t2)) | m_main_v_turn(s48, c_2)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4226, 760, 4223])).
% 1.16/1.17 tff(4228,plain,
% 1.16/1.17 (m_main_v_turn(s48, c_2)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4227, 4195, 4139])).
% 1.16/1.17 tff(4229,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4230,plain,
% 1.16/1.17 ((~![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)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4231,plain,
% 1.16/1.17 ((~![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))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4230, 4229])).
% 1.16/1.17 tff(4232,plain,
% 1.16/1.17 (~m_main_v_turn(s48, c_1)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4231, 156, 4228])).
% 1.16/1.17 tff(4233,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4234,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s48, c_1) | (~node5(s48)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4235,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s48, c_1) | (~node5(s48))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 1.16/1.17 tff(4236,plain,
% 1.16/1.17 (~node5(s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4235, 776, 4232])).
% 1.16/1.17 tff(4237,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4238,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s48, c_n1) | (~node2(s48)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4239,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s48, c_n1) | (~node2(s48))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.16/1.17 tff(4240,plain,
% 1.16/1.17 (~node2(s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4239, 787, 4215])).
% 1.16/1.17 tff(4241,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.17 inference(rewrite,[status(thm)],[])).
% 1.16/1.17 tff(4242,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s48, c_n1) | (~node3(s48)))),
% 1.16/1.17 inference(quant_inst,[status(thm)],[])).
% 1.16/1.17 tff(4243,plain,
% 1.16/1.17 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s48, c_n1) | (~node3(s48))),
% 1.16/1.17 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 1.16/1.17 tff(4244,plain,
% 1.16/1.17 (~node3(s48)),
% 1.16/1.17 inference(unit_resolution,[status(thm)],[4243, 798, 4215])).
% 1.16/1.17 tff(4245,plain,
% 1.16/1.17 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4246,plain,
% 1.16/1.18 ((~![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)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4247,plain,
% 1.16/1.18 ((~![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))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 1.16/1.18 tff(4248,plain,
% 1.16/1.18 (~m_main_v_state1(s48, c_c1)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4247, 539, 4211])).
% 1.16/1.18 tff(4249,plain,
% 1.16/1.18 (((~![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(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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4250,plain,
% 1.16/1.18 (((~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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4251,plain,
% 1.16/1.18 (((~![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))))),
% 1.16/1.18 inference(monotonicity,[status(thm)],[4250])).
% 1.16/1.18 tff(4252,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(transitivity,[status(thm)],[4251, 4249])).
% 1.16/1.18 tff(4253,plain,
% 1.16/1.18 ((~![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)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4254,plain,
% 1.16/1.18 ((~![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(s46, c_n2) | (~m_main_v_state2(s47, c_n2)) | (~node13(s46, s47))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4253, 4252])).
% 1.16/1.18 tff(4255,plain,
% 1.16/1.18 (~m_main_v_state2(s47, c_n2)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4254, 311, 4096, 4188])).
% 1.16/1.18 tff(4256,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4257,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s47, c_n2) | (~node9(s47)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4258,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s47, c_n2) | (~node9(s47))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4257, 4256])).
% 1.16/1.18 tff(4259,plain,
% 1.16/1.18 (~node9(s47)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4258, 88, 4255])).
% 1.16/1.18 tff(4260,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4261,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s47, c_n2) | (~node10(s47)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4262,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s47, c_n2) | (~node10(s47))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4261, 4260])).
% 1.16/1.18 tff(4263,plain,
% 1.16/1.18 (~node10(s47)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4262, 249, 4255])).
% 1.16/1.18 tff(4264,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4265,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s47, c_n2) | (~node8(s47)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4266,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s47, c_n2) | (~node8(s47))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 1.16/1.18 tff(4267,plain,
% 1.16/1.18 (~node8(s47)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4266, 271, 4255])).
% 1.16/1.18 tff(4268,plain,
% 1.16/1.18 (((~![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))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4269,plain,
% 1.16/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s47, s48)) | node14(s47, s48))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4270,plain,
% 1.16/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s47, s48)) | node14(s47, s48)),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4269, 4268])).
% 1.16/1.18 tff(4271,plain,
% 1.16/1.18 (node14(s47, s48)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4270, 7, 4202])).
% 1.16/1.18 tff(4272,plain,
% 1.16/1.18 (((~![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(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))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4273,plain,
% 1.16/1.18 ((~![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(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))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4274,plain,
% 1.16/1.18 ((~![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(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)),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 1.16/1.18 tff(4275,plain,
% 1.16/1.18 ((~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)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4274, 617, 4271])).
% 1.16/1.18 tff(4276,plain,
% 1.16/1.18 (m_main_v_state2(s48, c_c2)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4275, 4267, 4139, 4195, 4263, 4259])).
% 1.16/1.18 tff(4277,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4278,plain,
% 1.16/1.18 ((~![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)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4279,plain,
% 1.16/1.18 ((~![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))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 1.16/1.18 tff(4280,plain,
% 1.16/1.18 (~m_main_v_state2(s48, c_n2)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4279, 697, 4276])).
% 1.16/1.18 tff(4281,plain,
% 1.16/1.18 (((~![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)))),
% 1.16/1.18 inference(rewrite,[status(thm)],[])).
% 1.16/1.18 tff(4282,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s48, c_n2) | (~node4(s48)))),
% 1.16/1.18 inference(quant_inst,[status(thm)],[])).
% 1.16/1.18 tff(4283,plain,
% 1.16/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s48, c_n2) | (~node4(s48))),
% 1.16/1.18 inference(modus_ponens,[status(thm)],[4282, 4281])).
% 1.16/1.18 tff(4284,plain,
% 1.16/1.18 (~node4(s48)),
% 1.16/1.18 inference(unit_resolution,[status(thm)],[4283, 388, 4280])).
% 1.16/1.18 tff(4285,plain,
% 1.16/1.18 (succ(s48, s49) <=> succ(s48, s49)),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4286,axiom,(succ(s48, s49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound49')).
% 1.26/1.18 tff(4287,plain,
% 1.26/1.18 (succ(s48, s49)),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4286, 4285])).
% 1.26/1.18 tff(4288,plain,
% 1.26/1.18 (((~![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))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4289,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4290,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4289, 4288])).
% 1.26/1.18 tff(4291,plain,
% 1.26/1.18 (trans(s48, s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4290, 4287, 39])).
% 1.26/1.18 tff(4292,plain,
% 1.26/1.18 (((~![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))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4293,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s48, s49)) | node7(s48, s49))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4294,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s48, s49)) | node7(s48, s49)),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4293, 4292])).
% 1.26/1.18 tff(4295,plain,
% 1.26/1.18 (node7(s48, s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4294, 206, 4291])).
% 1.26/1.18 tff(4296,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4297,plain,
% 1.26/1.18 ((~![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)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4298,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4297, 4296])).
% 1.26/1.18 tff(4299,plain,
% 1.26/1.18 (m_main_v_state1(s48, c_c1) | node1(s48) | node2(s48) | node3(s48) | node4(s48) | node5(s48) | node6(s48, s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4298, 820, 4295])).
% 1.26/1.18 tff(4300,plain,
% 1.26/1.18 (node6(s48, s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4299, 4284, 4248, 4244, 4240, 4236, 4219])).
% 1.26/1.18 tff(4301,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4302,plain,
% 1.26/1.18 (((~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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4303,plain,
% 1.26/1.18 (((~![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))))),
% 1.26/1.18 inference(monotonicity,[status(thm)],[4302])).
% 1.26/1.18 tff(4304,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(transitivity,[status(thm)],[4303, 4301])).
% 1.26/1.18 tff(4305,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4306,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4305, 4304])).
% 1.26/1.18 tff(4307,plain,
% 1.26/1.18 (m_main_v_state1(s49, c_t1)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4306, 856, 4211, 4300])).
% 1.26/1.18 tff(4308,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4309,plain,
% 1.26/1.18 ((~![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)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4310,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 1.26/1.18 tff(4311,plain,
% 1.26/1.18 (~m_main_v_state2(s48, c_t2)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4310, 260, 4276])).
% 1.26/1.18 tff(4312,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4313,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s48, c_t2) | (~node12(s48)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4314,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s48, c_t2) | (~node12(s48))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 1.26/1.18 tff(4315,plain,
% 1.26/1.18 (~node12(s48)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4314, 633, 4311])).
% 1.26/1.18 tff(4316,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4317,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s48, c_n1) | (~node11(s48)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4318,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s48, c_n1) | (~node11(s48))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 1.26/1.18 tff(4319,plain,
% 1.26/1.18 (~node11(s48)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4318, 238, 4215])).
% 1.26/1.18 tff(4320,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4321,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s48, c_c1) | (~node10(s48)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4322,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s48, c_c1) | (~node10(s48))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 1.26/1.18 tff(4323,plain,
% 1.26/1.18 (~node10(s48)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4322, 675, 4248])).
% 1.26/1.18 tff(4324,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4325,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s48, c_n1) | (~node9(s48)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4326,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s48, c_n1) | (~node9(s48))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4325, 4324])).
% 1.26/1.18 tff(4327,plain,
% 1.26/1.18 (~node9(s48)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4326, 686, 4215])).
% 1.26/1.18 tff(4328,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4329,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s48, c_n2) | (~node8(s48)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4330,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s48, c_n2) | (~node8(s48))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4329, 4328])).
% 1.26/1.18 tff(4331,plain,
% 1.26/1.18 (~node8(s48)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4330, 271, 4280])).
% 1.26/1.18 tff(4332,plain,
% 1.26/1.18 (((~![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))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4333,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s48, s49)) | node14(s48, s49))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4334,plain,
% 1.26/1.18 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s48, s49)) | node14(s48, s49)),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4333, 4332])).
% 1.26/1.18 tff(4335,plain,
% 1.26/1.18 (node14(s48, s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4334, 7, 4291])).
% 1.26/1.18 tff(4336,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4337,plain,
% 1.26/1.18 (((~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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4338,plain,
% 1.26/1.18 (((~![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))))),
% 1.26/1.18 inference(monotonicity,[status(thm)],[4337])).
% 1.26/1.18 tff(4339,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(transitivity,[status(thm)],[4338, 4336])).
% 1.26/1.18 tff(4340,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4341,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 1.26/1.18 tff(4342,plain,
% 1.26/1.18 (m_main_v_state2(s49, c_n2) | node9(s48) | node8(s48) | node10(s48) | node11(s48) | node12(s48) | (~m_main_v_state2(s48, c_c2))),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4341, 726, 4335])).
% 1.26/1.18 tff(4343,plain,
% 1.26/1.18 (m_main_v_state2(s49, c_n2)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4342, 4331, 4276, 4327, 4323, 4319, 4315])).
% 1.26/1.18 tff(4344,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4345,plain,
% 1.26/1.18 ((~![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)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4346,plain,
% 1.26/1.18 ((~![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))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 1.26/1.18 tff(4347,plain,
% 1.26/1.18 (~m_main_v_state2(s49, c_t2)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4346, 77, 4343])).
% 1.26/1.18 tff(4348,plain,
% 1.26/1.18 (((~![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)))),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4349,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s49, c_t2) | (~node15(s49)))),
% 1.26/1.18 inference(quant_inst,[status(thm)],[])).
% 1.26/1.18 tff(4350,plain,
% 1.26/1.18 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s49, c_t2) | (~node15(s49))),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4349, 4348])).
% 1.26/1.18 tff(4351,plain,
% 1.26/1.18 (~node15(s49)),
% 1.26/1.18 inference(unit_resolution,[status(thm)],[4350, 103, 4347])).
% 1.26/1.18 tff(4352,plain,
% 1.26/1.18 (succ(s49, s50) <=> succ(s49, s50)),
% 1.26/1.18 inference(rewrite,[status(thm)],[])).
% 1.26/1.18 tff(4353,axiom,(succ(s49, s50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound50')).
% 1.26/1.18 tff(4354,plain,
% 1.26/1.18 (succ(s49, s50)),
% 1.26/1.18 inference(modus_ponens,[status(thm)],[4353, 4352])).
% 1.26/1.18 tff(4355,plain,
% 1.26/1.18 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4356,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4357,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4356, 4355])).
% 1.26/1.19 tff(4358,plain,
% 1.26/1.19 (trans(s49, s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4357, 4354, 39])).
% 1.26/1.19 tff(4359,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4360,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s49, s50)) | node18(s49, s50))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4361,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s49, s50)) | node18(s49, s50)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4360, 4359])).
% 1.26/1.19 tff(4362,plain,
% 1.26/1.19 (node18(s49, s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4361, 125, 4358])).
% 1.26/1.19 tff(4363,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4364,plain,
% 1.26/1.19 (((~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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4365,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(monotonicity,[status(thm)],[4364])).
% 1.26/1.19 tff(4366,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(transitivity,[status(thm)],[4365, 4363])).
% 1.26/1.19 tff(4367,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4368,plain,
% 1.26/1.19 ((~![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)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 1.26/1.19 tff(4369,plain,
% 1.26/1.19 (node15(s49) | (~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_turn(s50, c_1)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4368, 992, 4362])).
% 1.26/1.19 tff(4370,plain,
% 1.26/1.19 (m_main_v_turn(s50, c_1)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4369, 4351, 4343, 4307])).
% 1.26/1.19 tff(4371,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4372,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4373,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 1.26/1.19 tff(4374,plain,
% 1.26/1.19 (~m_main_v_turn(s50, c_2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4373, 156, 4370])).
% 1.26/1.19 tff(4375,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4376,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s50, c_2) | (~node12(s50)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4377,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s50, c_2) | (~node12(s50))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 1.26/1.19 tff(4378,plain,
% 1.26/1.19 (~node12(s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4377, 184, 4374])).
% 1.26/1.19 tff(4379,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4380,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s49, s50)) | node14(s49, s50))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4381,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s49, s50)) | node14(s49, s50)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 1.26/1.19 tff(4382,plain,
% 1.26/1.19 (node14(s49, s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4381, 7, 4358])).
% 1.26/1.19 tff(4383,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4384,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4385,plain,
% 1.26/1.19 ((~![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)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 1.26/1.19 tff(4386,plain,
% 1.26/1.19 ((~m_main_v_state1(s49, c_t1)) | (~m_main_v_state2(s49, c_n2)) | m_main_v_state2(s50, c_t2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4385, 922, 4382])).
% 1.26/1.19 tff(4387,plain,
% 1.26/1.19 (m_main_v_state2(s50, c_t2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4386, 4307, 4343])).
% 1.26/1.19 tff(4388,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4389,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4390,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4389, 4388])).
% 1.26/1.19 tff(4391,plain,
% 1.26/1.19 (~m_main_v_state2(s50, c_n2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4390, 77, 4387])).
% 1.26/1.19 tff(4392,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4393,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s50, c_n2) | (~node8(s50)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4394,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s50, c_n2) | (~node8(s50))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4393, 4392])).
% 1.26/1.19 tff(4395,plain,
% 1.26/1.19 (~node8(s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4394, 271, 4391])).
% 1.26/1.19 tff(4396,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4397,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s50, c_n2) | (~node9(s50)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4398,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s50, c_n2) | (~node9(s50))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 1.26/1.19 tff(4399,plain,
% 1.26/1.19 (~node9(s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4398, 88, 4391])).
% 1.26/1.19 tff(4400,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4401,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s50, c_n2) | (~node10(s50)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4402,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s50, c_n2) | (~node10(s50))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 1.26/1.19 tff(4403,plain,
% 1.26/1.19 (~node10(s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4402, 249, 4391])).
% 1.26/1.19 tff(4404,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4405,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4406,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 1.26/1.19 tff(4407,plain,
% 1.26/1.19 (~m_main_v_state2(s50, c_c2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4406, 260, 4387])).
% 1.26/1.19 tff(4408,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4409,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4410,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4409, 4408])).
% 1.26/1.19 tff(4411,plain,
% 1.26/1.19 (~m_main_v_state2(s49, c_c2)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4410, 697, 4343])).
% 1.26/1.19 tff(4412,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4413,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s49, c_c2) | (~node3(s49)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4414,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s49, c_c2) | (~node3(s49))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4413, 4412])).
% 1.26/1.19 tff(4415,plain,
% 1.26/1.19 (~node3(s49)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4414, 399, 4411])).
% 1.26/1.19 tff(4416,plain,
% 1.26/1.19 (((~![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(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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4417,plain,
% 1.26/1.19 (((~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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4418,plain,
% 1.26/1.19 (((~![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))))),
% 1.26/1.19 inference(monotonicity,[status(thm)],[4417])).
% 1.26/1.19 tff(4419,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(transitivity,[status(thm)],[4418, 4416])).
% 1.26/1.19 tff(4420,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4421,plain,
% 1.26/1.19 ((~![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(s48, c_n1) | (~m_main_v_state1(s49, c_n1)) | (~node6(s48, s49))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 1.26/1.19 tff(4422,plain,
% 1.26/1.19 (~m_main_v_state1(s49, c_n1)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4421, 835, 4215, 4300])).
% 1.26/1.19 tff(4423,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4424,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s49, c_n1) | (~node2(s49)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4425,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s49, c_n1) | (~node2(s49))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4424, 4423])).
% 1.26/1.19 tff(4426,plain,
% 1.26/1.19 (~node2(s49)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4425, 787, 4422])).
% 1.26/1.19 tff(4427,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4428,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s49, c_t2) | (~node1(s49)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4429,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s49, c_t2) | (~node1(s49))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4428, 4427])).
% 1.26/1.19 tff(4430,plain,
% 1.26/1.19 (~node1(s49)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4429, 195, 4347])).
% 1.26/1.19 tff(4431,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4432,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s49, s50)) | node7(s49, s50))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4433,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s49, s50)) | node7(s49, s50)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4432, 4431])).
% 1.26/1.19 tff(4434,plain,
% 1.26/1.19 (node7(s49, s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4433, 206, 4358])).
% 1.26/1.19 tff(4435,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4436,plain,
% 1.26/1.19 (((~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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4437,plain,
% 1.26/1.19 (((~![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))))),
% 1.26/1.19 inference(monotonicity,[status(thm)],[4436])).
% 1.26/1.19 tff(4438,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(transitivity,[status(thm)],[4437, 4435])).
% 1.26/1.19 tff(4439,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4440,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 1.26/1.19 tff(4441,plain,
% 1.26/1.19 ((~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)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4440, 892, 4434])).
% 1.26/1.19 tff(4442,plain,
% 1.26/1.19 (m_main_v_state1(s50, c_c1)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4441, 4430, 4343, 4307, 4426, 4415])).
% 1.26/1.19 tff(4443,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4444,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4445,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4444, 4443])).
% 1.26/1.19 tff(4446,plain,
% 1.26/1.19 (~m_main_v_state1(s50, c_n1)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4445, 454, 4442])).
% 1.26/1.19 tff(4447,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4448,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s50, c_n1) | (~node11(s50)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4449,plain,
% 1.26/1.19 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s50, c_n1) | (~node11(s50))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 1.26/1.19 tff(4450,plain,
% 1.26/1.19 (~node11(s50)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4449, 238, 4446])).
% 1.26/1.19 tff(4451,plain,
% 1.26/1.19 (succ(s50, s51) <=> succ(s50, s51)),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4452,axiom,(succ(s50, s51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound51')).
% 1.26/1.19 tff(4453,plain,
% 1.26/1.19 (succ(s50, s51)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4452, 4451])).
% 1.26/1.19 tff(4454,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4455,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4456,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 1.26/1.19 tff(4457,plain,
% 1.26/1.19 (trans(s50, s51)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4456, 4453, 39])).
% 1.26/1.19 tff(4458,plain,
% 1.26/1.19 (((~![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))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4459,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s50, s51)) | node14(s50, s51))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4460,plain,
% 1.26/1.19 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s50, s51)) | node14(s50, s51)),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 1.26/1.19 tff(4461,plain,
% 1.26/1.19 (node14(s50, s51)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4460, 7, 4457])).
% 1.26/1.19 tff(4462,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4463,plain,
% 1.26/1.19 ((~![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)))),
% 1.26/1.19 inference(quant_inst,[status(thm)],[])).
% 1.26/1.19 tff(4464,plain,
% 1.26/1.19 ((~![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))),
% 1.26/1.19 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 1.26/1.19 tff(4465,plain,
% 1.26/1.19 (m_main_v_state2(s50, c_c2) | node9(s50) | node8(s50) | node10(s50) | node11(s50) | node12(s50) | node13(s50, s51)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4464, 296, 4461])).
% 1.26/1.19 tff(4466,plain,
% 1.26/1.19 (node13(s50, s51)),
% 1.26/1.19 inference(unit_resolution,[status(thm)],[4465, 4450, 4407, 4403, 4399, 4395, 4378])).
% 1.26/1.19 tff(4467,plain,
% 1.26/1.19 (((~![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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4468,plain,
% 1.26/1.19 (((~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)))),
% 1.26/1.19 inference(rewrite,[status(thm)],[])).
% 1.26/1.19 tff(4469,plain,
% 1.26/1.19 (((~![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))))),
% 1.26/1.19 inference(monotonicity,[status(thm)],[4468])).
% 1.26/1.20 tff(4470,plain,
% 1.26/1.20 (((~![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)))),
% 1.26/1.20 inference(transitivity,[status(thm)],[4469, 4467])).
% 1.26/1.20 tff(4471,plain,
% 1.26/1.20 ((~![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)))),
% 1.26/1.20 inference(quant_inst,[status(thm)],[])).
% 1.26/1.20 tff(4472,plain,
% 1.26/1.20 ((~![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))),
% 1.26/1.20 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 1.26/1.20 tff(4473,plain,
% 1.26/1.20 (~m_main_v_state2(s51, c_n2)),
% 1.26/1.20 inference(unit_resolution,[status(thm)],[4472, 311, 4391, 4466])).
% 1.26/1.20 tff(4474,plain,
% 1.26/1.20 (((~![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)))),
% 1.26/1.20 inference(rewrite,[status(thm)],[])).
% 1.26/1.20 tff(4475,plain,
% 1.26/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s51, c_n2) | (~node9(s51)))),
% 1.26/1.20 inference(quant_inst,[status(thm)],[])).
% 1.26/1.20 tff(4476,plain,
% 1.26/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s51, c_n2) | (~node9(s51))),
% 1.26/1.20 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 1.26/1.20 tff(4477,plain,
% 1.26/1.20 (~node9(s51)),
% 1.26/1.20 inference(unit_resolution,[status(thm)],[4476, 88, 4473])).
% 1.26/1.20 tff(4478,plain,
% 1.26/1.20 (((~![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)))),
% 1.26/1.20 inference(rewrite,[status(thm)],[])).
% 1.26/1.20 tff(4479,plain,
% 1.26/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s51, c_n2) | (~node10(s51)))),
% 1.26/1.20 inference(quant_inst,[status(thm)],[])).
% 1.26/1.20 tff(4480,plain,
% 1.26/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s51, c_n2) | (~node10(s51))),
% 1.26/1.20 inference(modus_ponens,[status(thm)],[4479, 4478])).
% 1.26/1.20 tff(4481,plain,
% 1.26/1.20 (~node10(s51)),
% 1.26/1.20 inference(unit_resolution,[status(thm)],[4480, 249, 4473])).
% 1.26/1.20 tff(4482,plain,
% 1.26/1.20 (((~![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)))),
% 1.26/1.20 inference(rewrite,[status(thm)],[])).
% 1.26/1.20 tff(4483,plain,
% 1.26/1.20 (((~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)))),
% 1.26/1.20 inference(rewrite,[status(thm)],[])).
% 1.26/1.20 tff(4484,plain,
% 1.26/1.20 (((~![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))))),
% 1.26/1.20 inference(monotonicity,[status(thm)],[4483])).
% 1.26/1.20 tff(4485,plain,
% 1.26/1.20 (((~![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)))),
% 1.26/1.20 inference(transitivity,[status(thm)],[4484, 4482])).
% 1.28/1.20 tff(4486,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4487,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4486, 4485])).
% 1.28/1.20 tff(4488,plain,
% 1.28/1.20 (m_main_v_state2(s51, c_t2)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4487, 518, 4387, 4466])).
% 1.28/1.20 tff(4489,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4490,plain,
% 1.28/1.20 ((~![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)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4491,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4490, 4489])).
% 1.28/1.20 tff(4492,plain,
% 1.28/1.20 (~m_main_v_state1(s50, c_t1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4491, 539, 4442])).
% 1.28/1.20 tff(4493,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4494,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s50, c_t1) | (~node5(s50)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4495,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s50, c_t1) | (~node5(s50))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4494, 4493])).
% 1.28/1.20 tff(4496,plain,
% 1.28/1.20 (~node5(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4495, 550, 4492])).
% 1.28/1.20 tff(4497,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4498,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s50, c_n2) | (~node4(s50)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4499,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s50, c_n2) | (~node4(s50))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4498, 4497])).
% 1.28/1.20 tff(4500,plain,
% 1.28/1.20 (~node4(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4499, 388, 4391])).
% 1.28/1.20 tff(4501,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4502,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s50, c_c2) | (~node3(s50)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4503,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s50, c_c2) | (~node3(s50))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.28/1.20 tff(4504,plain,
% 1.28/1.20 (~node3(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4503, 399, 4407])).
% 1.28/1.20 tff(4505,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4506,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s50, c_n2) | (~node2(s50)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4507,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s50, c_n2) | (~node2(s50))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 1.28/1.20 tff(4508,plain,
% 1.28/1.20 (~node2(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4507, 410, 4391])).
% 1.28/1.20 tff(4509,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4510,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s50, c_n1) | (~node1(s50)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4511,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s50, c_n1) | (~node1(s50))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 1.28/1.20 tff(4512,plain,
% 1.28/1.20 (~node1(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4511, 421, 4446])).
% 1.28/1.20 tff(4513,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4514,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s50, s51)) | node7(s50, s51))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4515,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s50, s51)) | node7(s50, s51)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.28/1.20 tff(4516,plain,
% 1.28/1.20 (node7(s50, s51)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4515, 206, 4457])).
% 1.28/1.20 tff(4517,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4518,plain,
% 1.28/1.20 (((~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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4519,plain,
% 1.28/1.20 (((~![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))))),
% 1.28/1.20 inference(monotonicity,[status(thm)],[4518])).
% 1.28/1.20 tff(4520,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(transitivity,[status(thm)],[4519, 4517])).
% 1.28/1.20 tff(4521,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4522,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4521, 4520])).
% 1.28/1.20 tff(4523,plain,
% 1.28/1.20 (m_main_v_state1(s51, c_n1) | (~m_main_v_state1(s50, c_c1)) | node1(s50) | node2(s50) | node3(s50) | node4(s50) | node5(s50)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4522, 584, 4516])).
% 1.28/1.20 tff(4524,plain,
% 1.28/1.20 (m_main_v_state1(s51, c_n1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4523, 4512, 4442, 4508, 4504, 4500, 4496])).
% 1.28/1.20 tff(4525,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4526,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s51, c_n2) | (~node8(s51)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4527,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s51, c_n2) | (~node8(s51))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.28/1.20 tff(4528,plain,
% 1.28/1.20 (~node8(s51)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4527, 271, 4473])).
% 1.28/1.20 tff(4529,plain,
% 1.28/1.20 (succ(s51, s52) <=> succ(s51, s52)),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4530,axiom,(succ(s51, s52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound52')).
% 1.28/1.20 tff(4531,plain,
% 1.28/1.20 (succ(s51, s52)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 1.28/1.20 tff(4532,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4533,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4534,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4533, 4532])).
% 1.28/1.20 tff(4535,plain,
% 1.28/1.20 (trans(s51, s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4534, 4531, 39])).
% 1.28/1.20 tff(4536,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4537,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s51, s52)) | node14(s51, s52))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4538,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s51, s52)) | node14(s51, s52)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 1.28/1.20 tff(4539,plain,
% 1.28/1.20 (node14(s51, s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4538, 7, 4535])).
% 1.28/1.20 tff(4540,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4541,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4542,plain,
% 1.28/1.20 ((~![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)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4541, 4540])).
% 1.28/1.20 tff(4543,plain,
% 1.28/1.20 ((~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)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4542, 617, 4539])).
% 1.28/1.20 tff(4544,plain,
% 1.28/1.20 (m_main_v_state2(s52, c_c2)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4543, 4528, 4524, 4488, 4481, 4477])).
% 1.28/1.20 tff(4545,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4546,plain,
% 1.28/1.20 ((~![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)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4547,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4546, 4545])).
% 1.28/1.20 tff(4548,plain,
% 1.28/1.20 (~m_main_v_state2(s52, c_t2)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4547, 260, 4544])).
% 1.28/1.20 tff(4549,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4550,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s52, c_t2) | (~node12(s52)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4551,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s52, c_t2) | (~node12(s52))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4550, 4549])).
% 1.28/1.20 tff(4552,plain,
% 1.28/1.20 (~node12(s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4551, 633, 4548])).
% 1.28/1.20 tff(4553,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4554,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s51, s52)) | node7(s51, s52))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4555,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s51, s52)) | node7(s51, s52)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4554, 4553])).
% 1.28/1.20 tff(4556,plain,
% 1.28/1.20 (node7(s51, s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4555, 206, 4535])).
% 1.28/1.20 tff(4557,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4558,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4559,plain,
% 1.28/1.20 ((~![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)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4558, 4557])).
% 1.28/1.20 tff(4560,plain,
% 1.28/1.20 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_state1(s52, c_t1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4559, 651, 4556])).
% 1.28/1.20 tff(4561,plain,
% 1.28/1.20 (m_main_v_state1(s52, c_t1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4560, 4488, 4524])).
% 1.28/1.20 tff(4562,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4563,plain,
% 1.28/1.20 ((~![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)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4564,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 1.28/1.20 tff(4565,plain,
% 1.28/1.20 (~m_main_v_state1(s52, c_n1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4564, 17, 4561])).
% 1.28/1.20 tff(4566,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4567,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s52, c_n1) | (~node11(s52)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4568,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s52, c_n1) | (~node11(s52))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4567, 4566])).
% 1.28/1.20 tff(4569,plain,
% 1.28/1.20 (~node11(s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4568, 238, 4565])).
% 1.28/1.20 tff(4570,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4571,plain,
% 1.28/1.20 ((~![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)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4572,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 1.28/1.20 tff(4573,plain,
% 1.28/1.20 (~m_main_v_state1(s52, c_c1)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4572, 539, 4561])).
% 1.28/1.20 tff(4574,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4575,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s52, c_c1) | (~node10(s52)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4576,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s52, c_c1) | (~node10(s52))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4575, 4574])).
% 1.28/1.20 tff(4577,plain,
% 1.28/1.20 (~node10(s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4576, 675, 4573])).
% 1.28/1.20 tff(4578,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4579,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s52, c_n1) | (~node9(s52)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4580,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s52, c_n1) | (~node9(s52))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 1.28/1.20 tff(4581,plain,
% 1.28/1.20 (~node9(s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4580, 686, 4565])).
% 1.28/1.20 tff(4582,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4583,plain,
% 1.28/1.20 ((~![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)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4584,plain,
% 1.28/1.20 ((~![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))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4583, 4582])).
% 1.28/1.20 tff(4585,plain,
% 1.28/1.20 (~m_main_v_state2(s52, c_n2)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4584, 697, 4544])).
% 1.28/1.20 tff(4586,plain,
% 1.28/1.20 (((~![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)))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4587,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s52, c_n2) | (~node8(s52)))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4588,plain,
% 1.28/1.20 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s52, c_n2) | (~node8(s52))),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 1.28/1.20 tff(4589,plain,
% 1.28/1.20 (~node8(s52)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4588, 271, 4585])).
% 1.28/1.20 tff(4590,plain,
% 1.28/1.20 (succ(s52, s53) <=> succ(s52, s53)),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4591,axiom,(succ(s52, s53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound53')).
% 1.28/1.20 tff(4592,plain,
% 1.28/1.20 (succ(s52, s53)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4591, 4590])).
% 1.28/1.20 tff(4593,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4594,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4595,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4594, 4593])).
% 1.28/1.20 tff(4596,plain,
% 1.28/1.20 (trans(s52, s53)),
% 1.28/1.20 inference(unit_resolution,[status(thm)],[4595, 4592, 39])).
% 1.28/1.20 tff(4597,plain,
% 1.28/1.20 (((~![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))),
% 1.28/1.20 inference(rewrite,[status(thm)],[])).
% 1.28/1.20 tff(4598,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s52, s53)) | node14(s52, s53))),
% 1.28/1.20 inference(quant_inst,[status(thm)],[])).
% 1.28/1.20 tff(4599,plain,
% 1.28/1.20 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s52, s53)) | node14(s52, s53)),
% 1.28/1.20 inference(modus_ponens,[status(thm)],[4598, 4597])).
% 1.28/1.20 tff(4600,plain,
% 1.28/1.21 (node14(s52, s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4599, 7, 4596])).
% 1.28/1.21 tff(4601,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4602,plain,
% 1.28/1.21 (((~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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4603,plain,
% 1.28/1.21 (((~![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))))),
% 1.28/1.21 inference(monotonicity,[status(thm)],[4602])).
% 1.28/1.21 tff(4604,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(transitivity,[status(thm)],[4603, 4601])).
% 1.28/1.21 tff(4605,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4606,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 1.28/1.21 tff(4607,plain,
% 1.28/1.21 (m_main_v_state2(s53, c_n2) | node9(s52) | node8(s52) | node10(s52) | node11(s52) | node12(s52) | (~m_main_v_state2(s52, c_c2))),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4606, 726, 4600])).
% 1.28/1.21 tff(4608,plain,
% 1.28/1.21 (m_main_v_state2(s53, c_n2)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4607, 4589, 4544, 4581, 4577, 4569, 4552])).
% 1.28/1.21 tff(4609,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4610,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4611,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 1.28/1.21 tff(4612,plain,
% 1.28/1.21 (~m_main_v_state2(s53, c_c2)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4611, 697, 4608])).
% 1.28/1.21 tff(4613,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4614,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s53, c_c2) | (~node3(s53)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4615,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s53, c_c2) | (~node3(s53))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4614, 4613])).
% 1.28/1.21 tff(4616,plain,
% 1.28/1.21 (~node3(s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4615, 399, 4612])).
% 1.28/1.21 tff(4617,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4618,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s52, c_n1) | (~node1(s52)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4619,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s52, c_n1) | (~node1(s52))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 1.28/1.21 tff(4620,plain,
% 1.28/1.21 (~node1(s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4619, 421, 4565])).
% 1.28/1.21 tff(4621,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4622,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s51, s52)) | node18(s51, s52))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4623,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s51, s52)) | node18(s51, s52)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 1.28/1.21 tff(4624,plain,
% 1.28/1.21 (node18(s51, s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4623, 125, 4535])).
% 1.28/1.21 tff(4625,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4626,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4627,plain,
% 1.28/1.21 ((~![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)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4626, 4625])).
% 1.28/1.21 tff(4628,plain,
% 1.28/1.21 ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state2(s51, c_t2)) | m_main_v_turn(s52, c_2)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4627, 760, 4624])).
% 1.28/1.21 tff(4629,plain,
% 1.28/1.21 (m_main_v_turn(s52, c_2)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4628, 4488, 4524])).
% 1.28/1.21 tff(4630,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4631,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4632,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 1.28/1.21 tff(4633,plain,
% 1.28/1.21 (~m_main_v_turn(s52, c_1)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4632, 156, 4629])).
% 1.28/1.21 tff(4634,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4635,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s52, c_1) | (~node5(s52)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4636,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s52, c_1) | (~node5(s52))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 1.28/1.21 tff(4637,plain,
% 1.28/1.21 (~node5(s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4636, 776, 4633])).
% 1.28/1.21 tff(4638,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4639,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s52, c_n1) | (~node2(s52)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4640,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s52, c_n1) | (~node2(s52))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4639, 4638])).
% 1.28/1.21 tff(4641,plain,
% 1.28/1.21 (~node2(s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4640, 787, 4565])).
% 1.28/1.21 tff(4642,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4643,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s52, c_n1) | (~node3(s52)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4644,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s52, c_n1) | (~node3(s52))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4643, 4642])).
% 1.28/1.21 tff(4645,plain,
% 1.28/1.21 (~node3(s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4644, 798, 4565])).
% 1.28/1.21 tff(4646,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4647,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s52, c_n2) | (~node4(s52)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4648,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s52, c_n2) | (~node4(s52))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4647, 4646])).
% 1.28/1.21 tff(4649,plain,
% 1.28/1.21 (~node4(s52)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4648, 388, 4585])).
% 1.28/1.21 tff(4650,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4651,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s52, s53)) | node7(s52, s53))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4652,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s52, s53)) | node7(s52, s53)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.28/1.21 tff(4653,plain,
% 1.28/1.21 (node7(s52, s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4652, 206, 4596])).
% 1.28/1.21 tff(4654,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4655,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4656,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4655, 4654])).
% 1.28/1.21 tff(4657,plain,
% 1.28/1.21 (m_main_v_state1(s52, c_c1) | node1(s52) | node2(s52) | node3(s52) | node4(s52) | node5(s52) | node6(s52, s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4656, 820, 4653])).
% 1.28/1.21 tff(4658,plain,
% 1.28/1.21 (node6(s52, s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4657, 4649, 4573, 4645, 4641, 4637, 4620])).
% 1.28/1.21 tff(4659,plain,
% 1.28/1.21 (((~![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(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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4660,plain,
% 1.28/1.21 (((~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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4661,plain,
% 1.28/1.21 (((~![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))))),
% 1.28/1.21 inference(monotonicity,[status(thm)],[4660])).
% 1.28/1.21 tff(4662,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(transitivity,[status(thm)],[4661, 4659])).
% 1.28/1.21 tff(4663,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4664,plain,
% 1.28/1.21 ((~![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(s52, c_n1) | (~m_main_v_state1(s53, c_n1)) | (~node6(s52, s53))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4663, 4662])).
% 1.28/1.21 tff(4665,plain,
% 1.28/1.21 (~m_main_v_state1(s53, c_n1)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4664, 835, 4565, 4658])).
% 1.28/1.21 tff(4666,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4667,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s53, c_n1) | (~node2(s53)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4668,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s53, c_n1) | (~node2(s53))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4667, 4666])).
% 1.28/1.21 tff(4669,plain,
% 1.28/1.21 (~node2(s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4668, 787, 4665])).
% 1.28/1.21 tff(4670,plain,
% 1.28/1.21 (((~![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(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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4671,plain,
% 1.28/1.21 (((~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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4672,plain,
% 1.28/1.21 (((~![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))))),
% 1.28/1.21 inference(monotonicity,[status(thm)],[4671])).
% 1.28/1.21 tff(4673,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(transitivity,[status(thm)],[4672, 4670])).
% 1.28/1.21 tff(4674,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4675,plain,
% 1.28/1.21 ((~![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(s52, c_t1)) | m_main_v_state1(s53, c_t1) | (~node6(s52, s53))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 1.28/1.21 tff(4676,plain,
% 1.28/1.21 (m_main_v_state1(s53, c_t1)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4675, 856, 4561, 4658])).
% 1.28/1.21 tff(4677,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4678,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4679,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 1.28/1.21 tff(4680,plain,
% 1.28/1.21 (~m_main_v_state2(s53, c_t2)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4679, 77, 4608])).
% 1.28/1.21 tff(4681,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4682,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s53, c_t2) | (~node1(s53)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4683,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s53, c_t2) | (~node1(s53))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 1.28/1.21 tff(4684,plain,
% 1.28/1.21 (~node1(s53)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4683, 195, 4680])).
% 1.28/1.21 tff(4685,plain,
% 1.28/1.21 (succ(s53, s54) <=> succ(s53, s54)),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4686,axiom,(succ(s53, s54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound54')).
% 1.28/1.21 tff(4687,plain,
% 1.28/1.21 (succ(s53, s54)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4686, 4685])).
% 1.28/1.21 tff(4688,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4689,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4690,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 1.28/1.21 tff(4691,plain,
% 1.28/1.21 (trans(s53, s54)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4690, 4687, 39])).
% 1.28/1.21 tff(4692,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4693,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s53, s54)) | node7(s53, s54))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4694,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s53, s54)) | node7(s53, s54)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4693, 4692])).
% 1.28/1.21 tff(4695,plain,
% 1.28/1.21 (node7(s53, s54)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4694, 206, 4691])).
% 1.28/1.21 tff(4696,plain,
% 1.28/1.21 (((~![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(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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4697,plain,
% 1.28/1.21 (((~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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4698,plain,
% 1.28/1.21 (((~![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(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))))),
% 1.28/1.21 inference(monotonicity,[status(thm)],[4697])).
% 1.28/1.21 tff(4699,plain,
% 1.28/1.21 (((~![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(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)))),
% 1.28/1.21 inference(transitivity,[status(thm)],[4698, 4696])).
% 1.28/1.21 tff(4700,plain,
% 1.28/1.21 ((~![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(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))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4701,plain,
% 1.28/1.21 ((~![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(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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4700, 4699])).
% 1.28/1.21 tff(4702,plain,
% 1.28/1.21 ((~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)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4701, 892, 4695])).
% 1.28/1.21 tff(4703,plain,
% 1.28/1.21 (m_main_v_state1(s54, c_c1)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4702, 4684, 4608, 4676, 4669, 4616])).
% 1.28/1.21 tff(4704,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4705,plain,
% 1.28/1.21 ((~![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)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4706,plain,
% 1.28/1.21 ((~![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))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 1.28/1.21 tff(4707,plain,
% 1.28/1.21 (~m_main_v_state1(s54, c_t1)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4706, 539, 4703])).
% 1.28/1.21 tff(4708,plain,
% 1.28/1.21 (((~![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)))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4709,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s54, c_t1) | (~node5(s54)))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4710,plain,
% 1.28/1.21 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s54, c_t1) | (~node5(s54))),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4709, 4708])).
% 1.28/1.21 tff(4711,plain,
% 1.28/1.21 (~node5(s54)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4710, 550, 4707])).
% 1.28/1.21 tff(4712,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.21 inference(rewrite,[status(thm)],[])).
% 1.28/1.21 tff(4713,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s53, s54)) | node14(s53, s54))),
% 1.28/1.21 inference(quant_inst,[status(thm)],[])).
% 1.28/1.21 tff(4714,plain,
% 1.28/1.21 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s53, s54)) | node14(s53, s54)),
% 1.28/1.21 inference(modus_ponens,[status(thm)],[4713, 4712])).
% 1.28/1.21 tff(4715,plain,
% 1.28/1.21 (node14(s53, s54)),
% 1.28/1.21 inference(unit_resolution,[status(thm)],[4714, 7, 4691])).
% 1.28/1.21 tff(4716,plain,
% 1.28/1.21 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4717,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4718,plain,
% 1.28/1.22 ((~![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)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4717, 4716])).
% 1.28/1.22 tff(4719,plain,
% 1.28/1.22 ((~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_state2(s54, c_t2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4718, 922, 4715])).
% 1.28/1.22 tff(4720,plain,
% 1.28/1.22 (m_main_v_state2(s54, c_t2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4719, 4676, 4608])).
% 1.28/1.22 tff(4721,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4722,plain,
% 1.28/1.22 ((~![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)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4723,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4722, 4721])).
% 1.28/1.22 tff(4724,plain,
% 1.28/1.22 (~m_main_v_state2(s54, c_n2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4723, 77, 4720])).
% 1.28/1.22 tff(4725,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4726,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s54, c_n2) | (~node4(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4727,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s54, c_n2) | (~node4(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4726, 4725])).
% 1.28/1.22 tff(4728,plain,
% 1.28/1.22 (~node4(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4727, 388, 4724])).
% 1.28/1.22 tff(4729,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4730,plain,
% 1.28/1.22 ((~![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)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4731,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4730, 4729])).
% 1.28/1.22 tff(4732,plain,
% 1.28/1.22 (~m_main_v_state2(s54, c_c2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4731, 260, 4720])).
% 1.28/1.22 tff(4733,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4734,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s54, c_c2) | (~node3(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4735,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s54, c_c2) | (~node3(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 1.28/1.22 tff(4736,plain,
% 1.28/1.22 (~node3(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4735, 399, 4732])).
% 1.28/1.22 tff(4737,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4738,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s54, c_n2) | (~node2(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4739,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s54, c_n2) | (~node2(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4738, 4737])).
% 1.28/1.22 tff(4740,plain,
% 1.28/1.22 (~node2(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4739, 410, 4724])).
% 1.28/1.22 tff(4741,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4742,plain,
% 1.28/1.22 ((~![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)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4743,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4742, 4741])).
% 1.28/1.22 tff(4744,plain,
% 1.28/1.22 (~m_main_v_state1(s54, c_n1)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4743, 454, 4703])).
% 1.28/1.22 tff(4745,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4746,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s54, c_n1) | (~node1(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4747,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s54, c_n1) | (~node1(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 1.28/1.22 tff(4748,plain,
% 1.28/1.22 (~node1(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4747, 421, 4744])).
% 1.28/1.22 tff(4749,plain,
% 1.28/1.22 (succ(s54, s55) <=> succ(s54, s55)),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4750,axiom,(succ(s54, s55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound55')).
% 1.28/1.22 tff(4751,plain,
% 1.28/1.22 (succ(s54, s55)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 1.28/1.22 tff(4752,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4753,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4754,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4753, 4752])).
% 1.28/1.22 tff(4755,plain,
% 1.28/1.22 (trans(s54, s55)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4754, 4751, 39])).
% 1.28/1.22 tff(4756,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4757,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s54, s55)) | node7(s54, s55))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4758,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s54, s55)) | node7(s54, s55)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4757, 4756])).
% 1.28/1.22 tff(4759,plain,
% 1.28/1.22 (node7(s54, s55)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4758, 206, 4755])).
% 1.28/1.22 tff(4760,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4761,plain,
% 1.28/1.22 (((~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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4762,plain,
% 1.28/1.22 (((~![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))))),
% 1.28/1.22 inference(monotonicity,[status(thm)],[4761])).
% 1.28/1.22 tff(4763,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(transitivity,[status(thm)],[4762, 4760])).
% 1.28/1.22 tff(4764,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4765,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4764, 4763])).
% 1.28/1.22 tff(4766,plain,
% 1.28/1.22 (m_main_v_state1(s55, c_n1) | (~m_main_v_state1(s54, c_c1)) | node1(s54) | node2(s54) | node3(s54) | node4(s54) | node5(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4765, 584, 4759])).
% 1.28/1.22 tff(4767,plain,
% 1.28/1.22 (m_main_v_state1(s55, c_n1)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4766, 4748, 4703, 4740, 4736, 4728, 4711])).
% 1.28/1.22 tff(4768,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4769,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s53, c_t2) | (~node15(s53)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4770,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s53, c_t2) | (~node15(s53))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4769, 4768])).
% 1.28/1.22 tff(4771,plain,
% 1.28/1.22 (~node15(s53)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4770, 103, 4680])).
% 1.28/1.22 tff(4772,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4773,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s53, s54)) | node18(s53, s54))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4774,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s53, s54)) | node18(s53, s54)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 1.28/1.22 tff(4775,plain,
% 1.28/1.22 (node18(s53, s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4774, 125, 4691])).
% 1.28/1.22 tff(4776,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4777,plain,
% 1.28/1.22 (((~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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4778,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(monotonicity,[status(thm)],[4777])).
% 1.28/1.22 tff(4779,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(transitivity,[status(thm)],[4778, 4776])).
% 1.28/1.22 tff(4780,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4781,plain,
% 1.28/1.22 ((~![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)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4780, 4779])).
% 1.28/1.22 tff(4782,plain,
% 1.28/1.22 (node15(s53) | (~m_main_v_state1(s53, c_t1)) | (~m_main_v_state2(s53, c_n2)) | m_main_v_turn(s54, c_1)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4781, 992, 4775])).
% 1.28/1.22 tff(4783,plain,
% 1.28/1.22 (m_main_v_turn(s54, c_1)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4782, 4771, 4608, 4676])).
% 1.28/1.22 tff(4784,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4785,plain,
% 1.28/1.22 ((~![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)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4786,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 1.28/1.22 tff(4787,plain,
% 1.28/1.22 (~m_main_v_turn(s54, c_2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4786, 156, 4783])).
% 1.28/1.22 tff(4788,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4789,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s54, c_2) | (~node12(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4790,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s54, c_2) | (~node12(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 1.28/1.22 tff(4791,plain,
% 1.28/1.22 (~node12(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4790, 184, 4787])).
% 1.28/1.22 tff(4792,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4793,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s54, c_n2) | (~node8(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4794,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s54, c_n2) | (~node8(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4793, 4792])).
% 1.28/1.22 tff(4795,plain,
% 1.28/1.22 (~node8(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4794, 271, 4724])).
% 1.28/1.22 tff(4796,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4797,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s54, c_n2) | (~node9(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4798,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s54, c_n2) | (~node9(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4797, 4796])).
% 1.28/1.22 tff(4799,plain,
% 1.28/1.22 (~node9(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4798, 88, 4724])).
% 1.28/1.22 tff(4800,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4801,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s54, c_n2) | (~node10(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4802,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s54, c_n2) | (~node10(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4801, 4800])).
% 1.28/1.22 tff(4803,plain,
% 1.28/1.22 (~node10(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4802, 249, 4724])).
% 1.28/1.22 tff(4804,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4805,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s54, c_n1) | (~node11(s54)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4806,plain,
% 1.28/1.22 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s54, c_n1) | (~node11(s54))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4805, 4804])).
% 1.28/1.22 tff(4807,plain,
% 1.28/1.22 (~node11(s54)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4806, 238, 4744])).
% 1.28/1.22 tff(4808,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4809,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s54, s55)) | node14(s54, s55))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4810,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s54, s55)) | node14(s54, s55)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4809, 4808])).
% 1.28/1.22 tff(4811,plain,
% 1.28/1.22 (node14(s54, s55)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4810, 7, 4755])).
% 1.28/1.22 tff(4812,plain,
% 1.28/1.22 (((~![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(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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4813,plain,
% 1.28/1.22 ((~![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(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55)))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4814,plain,
% 1.28/1.22 ((~![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(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55) | (~node14(s54, s55))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4813, 4812])).
% 1.28/1.22 tff(4815,plain,
% 1.28/1.22 (m_main_v_state2(s54, c_c2) | node9(s54) | node8(s54) | node10(s54) | node11(s54) | node12(s54) | node13(s54, s55)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4814, 296, 4811])).
% 1.28/1.22 tff(4816,plain,
% 1.28/1.22 (node13(s54, s55)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4815, 4807, 4732, 4803, 4799, 4795, 4791])).
% 1.28/1.22 tff(4817,plain,
% 1.28/1.22 (((~![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(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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4818,plain,
% 1.28/1.22 (((~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)))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4819,plain,
% 1.28/1.22 (((~![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))))),
% 1.28/1.22 inference(monotonicity,[status(thm)],[4818])).
% 1.28/1.22 tff(4820,plain,
% 1.28/1.22 (((~![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)))),
% 1.28/1.22 inference(transitivity,[status(thm)],[4819, 4817])).
% 1.28/1.22 tff(4821,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4822,plain,
% 1.28/1.22 ((~![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(s54, c_t2)) | m_main_v_state2(s55, c_t2) | (~node13(s54, s55))),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4821, 4820])).
% 1.28/1.22 tff(4823,plain,
% 1.28/1.22 (m_main_v_state2(s55, c_t2)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4822, 518, 4720, 4816])).
% 1.28/1.22 tff(4824,plain,
% 1.28/1.22 (succ(s55, s56) <=> succ(s55, s56)),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4825,axiom,(succ(s55, s56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound56')).
% 1.28/1.22 tff(4826,plain,
% 1.28/1.22 (succ(s55, s56)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.28/1.22 tff(4827,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4828,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4829,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4828, 4827])).
% 1.28/1.22 tff(4830,plain,
% 1.28/1.22 (trans(s55, s56)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4829, 4826, 39])).
% 1.28/1.22 tff(4831,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4832,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s55, s56)) | node7(s55, s56))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4833,plain,
% 1.28/1.22 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s55, s56)) | node7(s55, s56)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 1.28/1.22 tff(4834,plain,
% 1.28/1.22 (node7(s55, s56)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4833, 206, 4830])).
% 1.28/1.22 tff(4835,plain,
% 1.28/1.22 (((~![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))),
% 1.28/1.22 inference(rewrite,[status(thm)],[])).
% 1.28/1.22 tff(4836,plain,
% 1.28/1.22 ((~![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))),
% 1.28/1.22 inference(quant_inst,[status(thm)],[])).
% 1.28/1.22 tff(4837,plain,
% 1.28/1.22 ((~![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)),
% 1.28/1.22 inference(modus_ponens,[status(thm)],[4836, 4835])).
% 1.28/1.22 tff(4838,plain,
% 1.28/1.22 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_state1(s56, c_t1)),
% 1.28/1.22 inference(unit_resolution,[status(thm)],[4837, 651, 4834])).
% 1.28/1.23 tff(4839,plain,
% 1.28/1.23 (m_main_v_state1(s56, c_t1)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4838, 4823, 4767])).
% 1.28/1.23 tff(4840,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4841,plain,
% 1.28/1.23 ((~![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)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4842,plain,
% 1.28/1.23 ((~![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))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 1.28/1.23 tff(4843,plain,
% 1.28/1.23 (~m_main_v_state1(s56, c_n1)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4842, 17, 4839])).
% 1.28/1.23 tff(4844,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4845,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s56, c_n1) | (~node1(s56)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4846,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s56, c_n1) | (~node1(s56))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4845, 4844])).
% 1.28/1.23 tff(4847,plain,
% 1.28/1.23 (~node1(s56)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4846, 421, 4843])).
% 1.28/1.23 tff(4848,plain,
% 1.28/1.23 (((~![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))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4849,plain,
% 1.28/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s55, s56)) | node18(s55, s56))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4850,plain,
% 1.28/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s55, s56)) | node18(s55, s56)),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4849, 4848])).
% 1.28/1.23 tff(4851,plain,
% 1.28/1.23 (node18(s55, s56)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4850, 125, 4830])).
% 1.28/1.23 tff(4852,plain,
% 1.28/1.23 (((~![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))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4853,plain,
% 1.28/1.23 ((~![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))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4854,plain,
% 1.28/1.23 ((~![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)),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4853, 4852])).
% 1.28/1.23 tff(4855,plain,
% 1.28/1.23 ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state2(s55, c_t2)) | m_main_v_turn(s56, c_2)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4854, 760, 4851])).
% 1.28/1.23 tff(4856,plain,
% 1.28/1.23 (m_main_v_turn(s56, c_2)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4855, 4823, 4767])).
% 1.28/1.23 tff(4857,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4858,plain,
% 1.28/1.23 ((~![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)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4859,plain,
% 1.28/1.23 ((~![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))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4858, 4857])).
% 1.28/1.23 tff(4860,plain,
% 1.28/1.23 (~m_main_v_turn(s56, c_1)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4859, 156, 4856])).
% 1.28/1.23 tff(4861,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4862,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s56, c_1) | (~node5(s56)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4863,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s56, c_1) | (~node5(s56))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 1.28/1.23 tff(4864,plain,
% 1.28/1.23 (~node5(s56)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4863, 776, 4860])).
% 1.28/1.23 tff(4865,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4866,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s56, c_n1) | (~node2(s56)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4867,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s56, c_n1) | (~node2(s56))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4866, 4865])).
% 1.28/1.23 tff(4868,plain,
% 1.28/1.23 (~node2(s56)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4867, 787, 4843])).
% 1.28/1.23 tff(4869,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4870,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s56, c_n1) | (~node3(s56)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4871,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s56, c_n1) | (~node3(s56))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4870, 4869])).
% 1.28/1.23 tff(4872,plain,
% 1.28/1.23 (~node3(s56)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4871, 798, 4843])).
% 1.28/1.23 tff(4873,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4874,plain,
% 1.28/1.23 ((~![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)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4875,plain,
% 1.28/1.23 ((~![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))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4874, 4873])).
% 1.28/1.23 tff(4876,plain,
% 1.28/1.23 (~m_main_v_state1(s56, c_c1)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4875, 539, 4839])).
% 1.28/1.23 tff(4877,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4878,plain,
% 1.28/1.23 (((~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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4879,plain,
% 1.28/1.23 (((~![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))))),
% 1.28/1.23 inference(monotonicity,[status(thm)],[4878])).
% 1.28/1.23 tff(4880,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(transitivity,[status(thm)],[4879, 4877])).
% 1.28/1.23 tff(4881,plain,
% 1.28/1.23 ((~![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)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4882,plain,
% 1.28/1.23 ((~![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))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 1.28/1.23 tff(4883,plain,
% 1.28/1.23 (~m_main_v_state2(s55, c_n2)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4882, 311, 4724, 4816])).
% 1.28/1.23 tff(4884,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4885,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s55, c_n2) | (~node9(s55)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4886,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s55, c_n2) | (~node9(s55))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 1.28/1.23 tff(4887,plain,
% 1.28/1.23 (~node9(s55)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4886, 88, 4883])).
% 1.28/1.23 tff(4888,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4889,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s55, c_n2) | (~node10(s55)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4890,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s55, c_n2) | (~node10(s55))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 1.28/1.23 tff(4891,plain,
% 1.28/1.23 (~node10(s55)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4890, 249, 4883])).
% 1.28/1.23 tff(4892,plain,
% 1.28/1.23 (((~![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)))),
% 1.28/1.23 inference(rewrite,[status(thm)],[])).
% 1.28/1.23 tff(4893,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s55, c_n2) | (~node8(s55)))),
% 1.28/1.23 inference(quant_inst,[status(thm)],[])).
% 1.28/1.23 tff(4894,plain,
% 1.28/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s55, c_n2) | (~node8(s55))),
% 1.28/1.23 inference(modus_ponens,[status(thm)],[4893, 4892])).
% 1.28/1.23 tff(4895,plain,
% 1.28/1.23 (~node8(s55)),
% 1.28/1.23 inference(unit_resolution,[status(thm)],[4894, 271, 4883])).
% 1.28/1.23 tff(4896,plain,
% 1.28/1.23 (((~![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))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4897,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s55, s56)) | node14(s55, s56))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4898,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s55, s56)) | node14(s55, s56)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4897, 4896])).
% 1.31/1.23 tff(4899,plain,
% 1.31/1.23 (node14(s55, s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4898, 7, 4830])).
% 1.31/1.23 tff(4900,plain,
% 1.31/1.23 (((~![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(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))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4901,plain,
% 1.31/1.23 ((~![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(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))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4902,plain,
% 1.31/1.23 ((~![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(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)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4901, 4900])).
% 1.31/1.23 tff(4903,plain,
% 1.31/1.23 ((~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)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4902, 617, 4899])).
% 1.31/1.23 tff(4904,plain,
% 1.31/1.23 (m_main_v_state2(s56, c_c2)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4903, 4895, 4767, 4823, 4891, 4887])).
% 1.31/1.23 tff(4905,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4906,plain,
% 1.31/1.23 ((~![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)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4907,plain,
% 1.31/1.23 ((~![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))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4906, 4905])).
% 1.31/1.23 tff(4908,plain,
% 1.31/1.23 (~m_main_v_state2(s56, c_n2)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4907, 697, 4904])).
% 1.31/1.23 tff(4909,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4910,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s56, c_n2) | (~node4(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4911,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s56, c_n2) | (~node4(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4910, 4909])).
% 1.31/1.23 tff(4912,plain,
% 1.31/1.23 (~node4(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4911, 388, 4908])).
% 1.31/1.23 tff(4913,plain,
% 1.31/1.23 (succ(s56, s57) <=> succ(s56, s57)),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4914,axiom,(succ(s56, s57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound57')).
% 1.31/1.23 tff(4915,plain,
% 1.31/1.23 (succ(s56, s57)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4914, 4913])).
% 1.31/1.23 tff(4916,plain,
% 1.31/1.23 (((~![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))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4917,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4918,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 1.31/1.23 tff(4919,plain,
% 1.31/1.23 (trans(s56, s57)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4918, 4915, 39])).
% 1.31/1.23 tff(4920,plain,
% 1.31/1.23 (((~![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))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4921,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s56, s57)) | node7(s56, s57))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4922,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s56, s57)) | node7(s56, s57)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4921, 4920])).
% 1.31/1.23 tff(4923,plain,
% 1.31/1.23 (node7(s56, s57)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4922, 206, 4919])).
% 1.31/1.23 tff(4924,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4925,plain,
% 1.31/1.23 ((~![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)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4926,plain,
% 1.31/1.23 ((~![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))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4925, 4924])).
% 1.31/1.23 tff(4927,plain,
% 1.31/1.23 (m_main_v_state1(s56, c_c1) | node1(s56) | node2(s56) | node3(s56) | node4(s56) | node5(s56) | node6(s56, s57)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4926, 820, 4923])).
% 1.31/1.23 tff(4928,plain,
% 1.31/1.23 (node6(s56, s57)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4927, 4912, 4876, 4872, 4868, 4864, 4847])).
% 1.31/1.23 tff(4929,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4930,plain,
% 1.31/1.23 (((~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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4931,plain,
% 1.31/1.23 (((~![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))))),
% 1.31/1.23 inference(monotonicity,[status(thm)],[4930])).
% 1.31/1.23 tff(4932,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(transitivity,[status(thm)],[4931, 4929])).
% 1.31/1.23 tff(4933,plain,
% 1.31/1.23 ((~![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))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4934,plain,
% 1.31/1.23 ((~![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))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4933, 4932])).
% 1.31/1.23 tff(4935,plain,
% 1.31/1.23 (m_main_v_state1(s57, c_t1)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4934, 856, 4839, 4928])).
% 1.31/1.23 tff(4936,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4937,plain,
% 1.31/1.23 ((~![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)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4938,plain,
% 1.31/1.23 ((~![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))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 1.31/1.23 tff(4939,plain,
% 1.31/1.23 (~m_main_v_state2(s56, c_t2)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4938, 260, 4904])).
% 1.31/1.23 tff(4940,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4941,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s56, c_t2) | (~node12(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4942,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s56, c_t2) | (~node12(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4941, 4940])).
% 1.31/1.23 tff(4943,plain,
% 1.31/1.23 (~node12(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4942, 633, 4939])).
% 1.31/1.23 tff(4944,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4945,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s56, c_n1) | (~node11(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4946,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s56, c_n1) | (~node11(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4945, 4944])).
% 1.31/1.23 tff(4947,plain,
% 1.31/1.23 (~node11(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4946, 238, 4843])).
% 1.31/1.23 tff(4948,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4949,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s56, c_c1) | (~node10(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4950,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s56, c_c1) | (~node10(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4949, 4948])).
% 1.31/1.23 tff(4951,plain,
% 1.31/1.23 (~node10(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4950, 675, 4876])).
% 1.31/1.23 tff(4952,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4953,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s56, c_n1) | (~node9(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4954,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s56, c_n1) | (~node9(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4953, 4952])).
% 1.31/1.23 tff(4955,plain,
% 1.31/1.23 (~node9(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4954, 686, 4843])).
% 1.31/1.23 tff(4956,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4957,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s56, c_n2) | (~node8(s56)))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4958,plain,
% 1.31/1.23 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s56, c_n2) | (~node8(s56))),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4957, 4956])).
% 1.31/1.23 tff(4959,plain,
% 1.31/1.23 (~node8(s56)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4958, 271, 4908])).
% 1.31/1.23 tff(4960,plain,
% 1.31/1.23 (((~![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))),
% 1.31/1.23 inference(rewrite,[status(thm)],[])).
% 1.31/1.23 tff(4961,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s56, s57)) | node14(s56, s57))),
% 1.31/1.23 inference(quant_inst,[status(thm)],[])).
% 1.31/1.23 tff(4962,plain,
% 1.31/1.23 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s56, s57)) | node14(s56, s57)),
% 1.31/1.23 inference(modus_ponens,[status(thm)],[4961, 4960])).
% 1.31/1.23 tff(4963,plain,
% 1.31/1.23 (node14(s56, s57)),
% 1.31/1.23 inference(unit_resolution,[status(thm)],[4962, 7, 4919])).
% 1.31/1.23 tff(4964,plain,
% 1.31/1.23 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4965,plain,
% 1.31/1.24 (((~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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4966,plain,
% 1.31/1.24 (((~![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(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))))),
% 1.31/1.24 inference(monotonicity,[status(thm)],[4965])).
% 1.31/1.24 tff(4967,plain,
% 1.31/1.24 (((~![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(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)))),
% 1.31/1.24 inference(transitivity,[status(thm)],[4966, 4964])).
% 1.31/1.24 tff(4968,plain,
% 1.31/1.24 ((~![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(s56, c_c2)) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | m_main_v_state2(s57, c_n2))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4969,plain,
% 1.31/1.24 ((~![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(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~node14(s56, s57)) | (~m_main_v_state2(s56, c_c2))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 1.31/1.24 tff(4970,plain,
% 1.31/1.24 (m_main_v_state2(s57, c_n2) | node9(s56) | node8(s56) | node10(s56) | node11(s56) | node12(s56) | (~m_main_v_state2(s56, c_c2))),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4969, 726, 4963])).
% 1.31/1.24 tff(4971,plain,
% 1.31/1.24 (m_main_v_state2(s57, c_n2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4970, 4959, 4904, 4955, 4951, 4947, 4943])).
% 1.31/1.24 tff(4972,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4973,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4974,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4973, 4972])).
% 1.31/1.24 tff(4975,plain,
% 1.31/1.24 (~m_main_v_state2(s57, c_t2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4974, 77, 4971])).
% 1.31/1.24 tff(4976,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4977,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s57, c_t2) | (~node15(s57)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4978,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s57, c_t2) | (~node15(s57))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 1.31/1.24 tff(4979,plain,
% 1.31/1.24 (~node15(s57)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4978, 103, 4975])).
% 1.31/1.24 tff(4980,plain,
% 1.31/1.24 (succ(s57, s58) <=> succ(s57, s58)),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4981,axiom,(succ(s57, s58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound58')).
% 1.31/1.24 tff(4982,plain,
% 1.31/1.24 (succ(s57, s58)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4981, 4980])).
% 1.31/1.24 tff(4983,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4984,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4985,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4984, 4983])).
% 1.31/1.24 tff(4986,plain,
% 1.31/1.24 (trans(s57, s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4985, 4982, 39])).
% 1.31/1.24 tff(4987,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4988,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s57, s58)) | node18(s57, s58))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4989,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s57, s58)) | node18(s57, s58)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 1.31/1.24 tff(4990,plain,
% 1.31/1.24 (node18(s57, s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4989, 125, 4986])).
% 1.31/1.24 tff(4991,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4992,plain,
% 1.31/1.24 (((~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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(4993,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(monotonicity,[status(thm)],[4992])).
% 1.31/1.24 tff(4994,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(transitivity,[status(thm)],[4993, 4991])).
% 1.31/1.24 tff(4995,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(4996,plain,
% 1.31/1.24 ((~![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)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[4995, 4994])).
% 1.31/1.24 tff(4997,plain,
% 1.31/1.24 (node15(s57) | (~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_turn(s58, c_1)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4996, 992, 4990])).
% 1.31/1.24 tff(4998,plain,
% 1.31/1.24 (m_main_v_turn(s58, c_1)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[4997, 4979, 4971, 4935])).
% 1.31/1.24 tff(4999,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5000,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5001,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 1.31/1.24 tff(5002,plain,
% 1.31/1.24 (~m_main_v_turn(s58, c_2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5001, 156, 4998])).
% 1.31/1.24 tff(5003,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5004,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s58, c_2) | (~node12(s58)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5005,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s58, c_2) | (~node12(s58))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5004, 5003])).
% 1.31/1.24 tff(5006,plain,
% 1.31/1.24 (~node12(s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5005, 184, 5002])).
% 1.31/1.24 tff(5007,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5008,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s57, s58)) | node14(s57, s58))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5009,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s57, s58)) | node14(s57, s58)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5008, 5007])).
% 1.31/1.24 tff(5010,plain,
% 1.31/1.24 (node14(s57, s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5009, 7, 4986])).
% 1.31/1.24 tff(5011,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5012,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5013,plain,
% 1.31/1.24 ((~![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)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5012, 5011])).
% 1.31/1.24 tff(5014,plain,
% 1.31/1.24 ((~m_main_v_state1(s57, c_t1)) | (~m_main_v_state2(s57, c_n2)) | m_main_v_state2(s58, c_t2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5013, 922, 5010])).
% 1.31/1.24 tff(5015,plain,
% 1.31/1.24 (m_main_v_state2(s58, c_t2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5014, 4935, 4971])).
% 1.31/1.24 tff(5016,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5017,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5018,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5017, 5016])).
% 1.31/1.24 tff(5019,plain,
% 1.31/1.24 (~m_main_v_state2(s58, c_n2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5018, 77, 5015])).
% 1.31/1.24 tff(5020,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5021,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s58, c_n2) | (~node8(s58)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5022,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s58, c_n2) | (~node8(s58))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5021, 5020])).
% 1.31/1.24 tff(5023,plain,
% 1.31/1.24 (~node8(s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5022, 271, 5019])).
% 1.31/1.24 tff(5024,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5025,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s58, c_n2) | (~node9(s58)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5026,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s58, c_n2) | (~node9(s58))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.31/1.24 tff(5027,plain,
% 1.31/1.24 (~node9(s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5026, 88, 5019])).
% 1.31/1.24 tff(5028,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5029,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s58, c_n2) | (~node10(s58)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5030,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s58, c_n2) | (~node10(s58))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5029, 5028])).
% 1.31/1.24 tff(5031,plain,
% 1.31/1.24 (~node10(s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5030, 249, 5019])).
% 1.31/1.24 tff(5032,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5033,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5034,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5033, 5032])).
% 1.31/1.24 tff(5035,plain,
% 1.31/1.24 (~m_main_v_state2(s58, c_c2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5034, 260, 5015])).
% 1.31/1.24 tff(5036,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5037,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5038,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 1.31/1.24 tff(5039,plain,
% 1.31/1.24 (~m_main_v_state2(s57, c_c2)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5038, 697, 4971])).
% 1.31/1.24 tff(5040,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5041,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s57, c_c2) | (~node3(s57)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5042,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s57, c_c2) | (~node3(s57))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5041, 5040])).
% 1.31/1.24 tff(5043,plain,
% 1.31/1.24 (~node3(s57)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5042, 399, 5039])).
% 1.31/1.24 tff(5044,plain,
% 1.31/1.24 (((~![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_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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5045,plain,
% 1.31/1.24 (((~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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5046,plain,
% 1.31/1.24 (((~![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))))),
% 1.31/1.24 inference(monotonicity,[status(thm)],[5045])).
% 1.31/1.24 tff(5047,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(transitivity,[status(thm)],[5046, 5044])).
% 1.31/1.24 tff(5048,plain,
% 1.31/1.24 ((~![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)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5049,plain,
% 1.31/1.24 ((~![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_n1) | (~m_main_v_state1(s57, c_n1)) | (~node6(s56, s57))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5048, 5047])).
% 1.31/1.24 tff(5050,plain,
% 1.31/1.24 (~m_main_v_state1(s57, c_n1)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5049, 835, 4843, 4928])).
% 1.31/1.24 tff(5051,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5052,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s57, c_n1) | (~node2(s57)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5053,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s57, c_n1) | (~node2(s57))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 1.31/1.24 tff(5054,plain,
% 1.31/1.24 (~node2(s57)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5053, 787, 5050])).
% 1.31/1.24 tff(5055,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5056,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s57, c_t2) | (~node1(s57)))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5057,plain,
% 1.31/1.24 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s57, c_t2) | (~node1(s57))),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5056, 5055])).
% 1.31/1.24 tff(5058,plain,
% 1.31/1.24 (~node1(s57)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5057, 195, 4975])).
% 1.31/1.24 tff(5059,plain,
% 1.31/1.24 (((~![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))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5060,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s57, s58)) | node7(s57, s58))),
% 1.31/1.24 inference(quant_inst,[status(thm)],[])).
% 1.31/1.24 tff(5061,plain,
% 1.31/1.24 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s57, s58)) | node7(s57, s58)),
% 1.31/1.24 inference(modus_ponens,[status(thm)],[5060, 5059])).
% 1.31/1.24 tff(5062,plain,
% 1.31/1.24 (node7(s57, s58)),
% 1.31/1.24 inference(unit_resolution,[status(thm)],[5061, 206, 4986])).
% 1.31/1.24 tff(5063,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5064,plain,
% 1.31/1.24 (((~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)))),
% 1.31/1.24 inference(rewrite,[status(thm)],[])).
% 1.31/1.24 tff(5065,plain,
% 1.31/1.24 (((~![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))))),
% 1.31/1.24 inference(monotonicity,[status(thm)],[5064])).
% 1.31/1.24 tff(5066,plain,
% 1.31/1.24 (((~![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)))),
% 1.31/1.24 inference(transitivity,[status(thm)],[5065, 5063])).
% 1.31/1.24 tff(5067,plain,
% 1.31/1.24 ((~![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))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5068,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5067, 5066])).
% 1.31/1.25 tff(5069,plain,
% 1.31/1.25 ((~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)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5068, 892, 5062])).
% 1.31/1.25 tff(5070,plain,
% 1.31/1.25 (m_main_v_state1(s58, c_c1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5069, 5058, 4971, 4935, 5054, 5043])).
% 1.31/1.25 tff(5071,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5072,plain,
% 1.31/1.25 ((~![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)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5073,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5072, 5071])).
% 1.31/1.25 tff(5074,plain,
% 1.31/1.25 (~m_main_v_state1(s58, c_n1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5073, 454, 5070])).
% 1.31/1.25 tff(5075,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5076,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s58, c_n1) | (~node11(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5077,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s58, c_n1) | (~node11(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 1.31/1.25 tff(5078,plain,
% 1.31/1.25 (~node11(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5077, 238, 5074])).
% 1.31/1.25 tff(5079,plain,
% 1.31/1.25 (succ(s58, s59) <=> succ(s58, s59)),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5080,axiom,(succ(s58, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound59')).
% 1.31/1.25 tff(5081,plain,
% 1.31/1.25 (succ(s58, s59)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5080, 5079])).
% 1.31/1.25 tff(5082,plain,
% 1.31/1.25 (((~![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))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5083,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5084,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5083, 5082])).
% 1.31/1.25 tff(5085,plain,
% 1.31/1.25 (trans(s58, s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5084, 5081, 39])).
% 1.31/1.25 tff(5086,plain,
% 1.31/1.25 (((~![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))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5087,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s58, s59)) | node14(s58, s59))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5088,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s58, s59)) | node14(s58, s59)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 1.31/1.25 tff(5089,plain,
% 1.31/1.25 (node14(s58, s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5088, 7, 5085])).
% 1.31/1.25 tff(5090,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5091,plain,
% 1.31/1.25 ((~![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)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5092,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5091, 5090])).
% 1.31/1.25 tff(5093,plain,
% 1.31/1.25 (m_main_v_state2(s58, c_c2) | node9(s58) | node8(s58) | node10(s58) | node11(s58) | node12(s58) | node13(s58, s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5092, 296, 5089])).
% 1.31/1.25 tff(5094,plain,
% 1.31/1.25 (node13(s58, s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5093, 5078, 5035, 5031, 5027, 5023, 5006])).
% 1.31/1.25 tff(5095,plain,
% 1.31/1.25 (((~![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) | (~m_main_v_state2(s59, c_n2)) | (~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_n2) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5096,plain,
% 1.31/1.25 (((~node13(s58, s59)) | m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2))) <=> (m_main_v_state2(s58, c_n2) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5097,plain,
% 1.31/1.25 (((~![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) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59))))),
% 1.31/1.25 inference(monotonicity,[status(thm)],[5096])).
% 1.31/1.25 tff(5098,plain,
% 1.31/1.25 (((~![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) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59)))),
% 1.31/1.25 inference(transitivity,[status(thm)],[5097, 5095])).
% 1.31/1.25 tff(5099,plain,
% 1.31/1.25 ((~![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)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5100,plain,
% 1.31/1.25 ((~![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) | (~m_main_v_state2(s59, c_n2)) | (~node13(s58, s59))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5099, 5098])).
% 1.31/1.25 tff(5101,plain,
% 1.31/1.25 (~m_main_v_state2(s59, c_n2)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5100, 311, 5019, 5094])).
% 1.31/1.25 tff(5102,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5103,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s59, c_n2) | (~node9(s59)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5104,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s59, c_n2) | (~node9(s59))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5103, 5102])).
% 1.31/1.25 tff(5105,plain,
% 1.31/1.25 (~node9(s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5104, 88, 5101])).
% 1.31/1.25 tff(5106,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5107,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s59, c_n2) | (~node10(s59)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5108,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s59, c_n2) | (~node10(s59))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5107, 5106])).
% 1.31/1.25 tff(5109,plain,
% 1.31/1.25 (~node10(s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5108, 249, 5101])).
% 1.31/1.25 tff(5110,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5111,plain,
% 1.31/1.25 (((~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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5112,plain,
% 1.31/1.25 (((~![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))))),
% 1.31/1.25 inference(monotonicity,[status(thm)],[5111])).
% 1.31/1.25 tff(5113,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(transitivity,[status(thm)],[5112, 5110])).
% 1.31/1.25 tff(5114,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5115,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5114, 5113])).
% 1.31/1.25 tff(5116,plain,
% 1.31/1.25 (m_main_v_state2(s59, c_t2)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5115, 518, 5015, 5094])).
% 1.31/1.25 tff(5117,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5118,plain,
% 1.31/1.25 ((~![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)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5119,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5118, 5117])).
% 1.31/1.25 tff(5120,plain,
% 1.31/1.25 (~m_main_v_state1(s58, c_t1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5119, 539, 5070])).
% 1.31/1.25 tff(5121,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5122,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s58, c_t1) | (~node5(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5123,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s58, c_t1) | (~node5(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5122, 5121])).
% 1.31/1.25 tff(5124,plain,
% 1.31/1.25 (~node5(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5123, 550, 5120])).
% 1.31/1.25 tff(5125,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5126,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s58, c_n2) | (~node4(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5127,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s58, c_n2) | (~node4(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5126, 5125])).
% 1.31/1.25 tff(5128,plain,
% 1.31/1.25 (~node4(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5127, 388, 5019])).
% 1.31/1.25 tff(5129,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5130,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s58, c_c2) | (~node3(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5131,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s58, c_c2) | (~node3(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5130, 5129])).
% 1.31/1.25 tff(5132,plain,
% 1.31/1.25 (~node3(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5131, 399, 5035])).
% 1.31/1.25 tff(5133,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5134,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s58, c_n2) | (~node2(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5135,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s58, c_n2) | (~node2(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5134, 5133])).
% 1.31/1.25 tff(5136,plain,
% 1.31/1.25 (~node2(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5135, 410, 5019])).
% 1.31/1.25 tff(5137,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5138,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s58, c_n1) | (~node1(s58)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5139,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s58, c_n1) | (~node1(s58))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5138, 5137])).
% 1.31/1.25 tff(5140,plain,
% 1.31/1.25 (~node1(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5139, 421, 5074])).
% 1.31/1.25 tff(5141,plain,
% 1.31/1.25 (((~![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))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5142,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s58, s59)) | node7(s58, s59))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5143,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s58, s59)) | node7(s58, s59)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5142, 5141])).
% 1.31/1.25 tff(5144,plain,
% 1.31/1.25 (node7(s58, s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5143, 206, 5085])).
% 1.31/1.25 tff(5145,plain,
% 1.31/1.25 (((~![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(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)))) <=> ((~![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(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5146,plain,
% 1.31/1.25 (((~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)) <=> (m_main_v_state1(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5147,plain,
% 1.31/1.25 (((~![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(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59))))),
% 1.31/1.25 inference(monotonicity,[status(thm)],[5146])).
% 1.31/1.25 tff(5148,plain,
% 1.31/1.25 (((~![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(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59)))),
% 1.31/1.25 inference(transitivity,[status(thm)],[5147, 5145])).
% 1.31/1.25 tff(5149,plain,
% 1.31/1.25 ((~![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))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5150,plain,
% 1.31/1.25 ((~![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(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58) | (~node7(s58, s59))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 1.31/1.25 tff(5151,plain,
% 1.31/1.25 (m_main_v_state1(s59, c_n1) | (~m_main_v_state1(s58, c_c1)) | node1(s58) | node2(s58) | node3(s58) | node4(s58) | node5(s58)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5150, 584, 5144])).
% 1.31/1.25 tff(5152,plain,
% 1.31/1.25 (m_main_v_state1(s59, c_n1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5151, 5140, 5070, 5136, 5132, 5128, 5124])).
% 1.31/1.25 tff(5153,plain,
% 1.31/1.25 (((~![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)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5154,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s59, c_n2) | (~node8(s59)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5155,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s59, c_n2) | (~node8(s59))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 1.31/1.25 tff(5156,plain,
% 1.31/1.25 (~node8(s59)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5155, 271, 5101])).
% 1.31/1.25 tff(5157,plain,
% 1.31/1.25 (succ(s59, s60) <=> succ(s59, s60)),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5158,axiom,(succ(s59, s60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound60')).
% 1.31/1.25 tff(5159,plain,
% 1.31/1.25 (succ(s59, s60)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 1.31/1.25 tff(5160,plain,
% 1.31/1.25 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5161,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5162,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5161, 5160])).
% 1.31/1.25 tff(5163,plain,
% 1.31/1.25 (trans(s59, s60)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5162, 5159, 39])).
% 1.31/1.25 tff(5164,plain,
% 1.31/1.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s59, s60)) | node14(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s59, s60)) | node14(s59, s60))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5165,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s59, s60)) | node14(s59, s60))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5166,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s59, s60)) | node14(s59, s60)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5165, 5164])).
% 1.31/1.25 tff(5167,plain,
% 1.31/1.25 (node14(s59, s60)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5166, 7, 5163])).
% 1.31/1.25 tff(5168,plain,
% 1.31/1.25 (((~![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, s60)) | m_main_v_state2(s60, 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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | (~node14(s59, s60)) | m_main_v_state2(s60, c_c2))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5169,plain,
% 1.31/1.25 ((~![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, s60)) | m_main_v_state2(s60, c_c2))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5170,plain,
% 1.31/1.25 ((~![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, s60)) | m_main_v_state2(s60, c_c2)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5169, 5168])).
% 1.31/1.25 tff(5171,plain,
% 1.31/1.25 ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | node9(s59) | node8(s59) | node10(s59) | m_main_v_state2(s60, c_c2)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5170, 617, 5167])).
% 1.31/1.25 tff(5172,plain,
% 1.31/1.25 (m_main_v_state2(s60, c_c2)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5171, 5156, 5152, 5116, 5109, 5105])).
% 1.31/1.25 tff(5173,plain,
% 1.31/1.25 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s60, c_t2)) | (~m_main_v_state2(s60, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s60, c_t2)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5174,plain,
% 1.31/1.25 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s60, c_t2)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5175,plain,
% 1.31/1.25 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s60, c_t2)) | (~m_main_v_state2(s60, c_c2))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5174, 5173])).
% 1.31/1.25 tff(5176,plain,
% 1.31/1.25 (~m_main_v_state2(s60, c_t2)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5175, 260, 5172])).
% 1.31/1.25 tff(5177,plain,
% 1.31/1.25 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s60, c_t2) | (~node12(s60)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s60, c_t2) | (~node12(s60)))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5178,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s60, c_t2) | (~node12(s60)))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5179,plain,
% 1.31/1.25 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s60, c_t2) | (~node12(s60))),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5178, 5177])).
% 1.31/1.25 tff(5180,plain,
% 1.31/1.25 (~node12(s60)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5179, 633, 5176])).
% 1.31/1.25 tff(5181,plain,
% 1.31/1.25 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s59, s60)) | node7(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s59, s60)) | node7(s59, s60))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5182,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s59, s60)) | node7(s59, s60))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5183,plain,
% 1.31/1.25 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s59, s60)) | node7(s59, s60)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 1.31/1.25 tff(5184,plain,
% 1.31/1.25 (node7(s59, s60)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5183, 206, 5163])).
% 1.31/1.25 tff(5185,plain,
% 1.31/1.25 (((~![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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, 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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, c_t1))),
% 1.31/1.25 inference(rewrite,[status(thm)],[])).
% 1.31/1.25 tff(5186,plain,
% 1.31/1.25 ((~![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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, c_t1))),
% 1.31/1.25 inference(quant_inst,[status(thm)],[])).
% 1.31/1.25 tff(5187,plain,
% 1.31/1.25 ((~![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(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | (~node7(s59, s60)) | m_main_v_state1(s60, c_t1)),
% 1.31/1.25 inference(modus_ponens,[status(thm)],[5186, 5185])).
% 1.31/1.25 tff(5188,plain,
% 1.31/1.25 ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | m_main_v_state1(s60, c_t1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5187, 651, 5184])).
% 1.31/1.25 tff(5189,plain,
% 1.31/1.25 (m_main_v_state1(s60, c_t1)),
% 1.31/1.25 inference(unit_resolution,[status(thm)],[5188, 5116, 5152])).
% 1.31/1.25 tff(5190,plain,
% 1.31/1.25 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s60, c_n1)) | (~m_main_v_state1(s60, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s60, c_n1)) | (~m_main_v_state1(s60, c_t1)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5191,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s60, c_n1)) | (~m_main_v_state1(s60, c_t1)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5192,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s60, c_n1)) | (~m_main_v_state1(s60, c_t1))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5191, 5190])).
% 1.31/1.26 tff(5193,plain,
% 1.31/1.26 (~m_main_v_state1(s60, c_n1)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5192, 17, 5189])).
% 1.31/1.26 tff(5194,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s60, c_n1) | (~node11(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s60, c_n1) | (~node11(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5195,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s60, c_n1) | (~node11(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5196,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s60, c_n1) | (~node11(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 1.31/1.26 tff(5197,plain,
% 1.31/1.26 (~node11(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5196, 238, 5193])).
% 1.31/1.26 tff(5198,plain,
% 1.31/1.26 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s60, c_t1)) | (~m_main_v_state1(s60, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s60, c_t1)) | (~m_main_v_state1(s60, c_c1)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5199,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s60, c_t1)) | (~m_main_v_state1(s60, c_c1)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5200,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s60, c_t1)) | (~m_main_v_state1(s60, c_c1))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5199, 5198])).
% 1.31/1.26 tff(5201,plain,
% 1.31/1.26 (~m_main_v_state1(s60, c_c1)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5200, 539, 5189])).
% 1.31/1.26 tff(5202,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s60, c_c1) | (~node10(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s60, c_c1) | (~node10(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5203,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s60, c_c1) | (~node10(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5204,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s60, c_c1) | (~node10(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5203, 5202])).
% 1.31/1.26 tff(5205,plain,
% 1.31/1.26 (~node10(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5204, 675, 5201])).
% 1.31/1.26 tff(5206,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s60, c_n1) | (~node9(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s60, c_n1) | (~node9(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5207,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s60, c_n1) | (~node9(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5208,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s60, c_n1) | (~node9(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5207, 5206])).
% 1.31/1.26 tff(5209,plain,
% 1.31/1.26 (~node9(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5208, 686, 5193])).
% 1.31/1.26 tff(5210,plain,
% 1.31/1.26 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s60, c_n2)) | (~m_main_v_state2(s60, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s60, c_n2)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5211,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s60, c_n2)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5212,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s60, c_n2)) | (~m_main_v_state2(s60, c_c2))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5211, 5210])).
% 1.31/1.26 tff(5213,plain,
% 1.31/1.26 (~m_main_v_state2(s60, c_n2)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5212, 697, 5172])).
% 1.31/1.26 tff(5214,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s60, c_n2) | (~node8(s60)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s60, c_n2) | (~node8(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5215,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s60, c_n2) | (~node8(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5216,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s60, c_n2) | (~node8(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5215, 5214])).
% 1.31/1.26 tff(5217,plain,
% 1.31/1.26 (~node8(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5216, 271, 5213])).
% 1.31/1.26 tff(5218,plain,
% 1.31/1.26 (succ(s60, s61) <=> succ(s60, s61)),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5219,axiom,(succ(s60, s61)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound61')).
% 1.31/1.26 tff(5220,plain,
% 1.31/1.26 (succ(s60, s61)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5219, 5218])).
% 1.31/1.26 tff(5221,plain,
% 1.31/1.26 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5222,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5223,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5222, 5221])).
% 1.31/1.26 tff(5224,plain,
% 1.31/1.26 (trans(s60, s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5223, 5220, 39])).
% 1.31/1.26 tff(5225,plain,
% 1.31/1.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s60, s61)) | node14(s60, s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s60, s61)) | node14(s60, s61))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5226,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s60, s61)) | node14(s60, s61))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5227,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s60, s61)) | node14(s60, s61)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5226, 5225])).
% 1.31/1.26 tff(5228,plain,
% 1.31/1.26 (node14(s60, s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5227, 7, 5224])).
% 1.31/1.26 tff(5229,plain,
% 1.31/1.26 (((~![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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, 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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5230,plain,
% 1.31/1.26 (((~m_main_v_state2(s60, c_c2)) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | m_main_v_state2(s61, c_n2)) <=> (m_main_v_state2(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5231,plain,
% 1.31/1.26 (((~![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(s60, c_c2)) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | m_main_v_state2(s61, 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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2))))),
% 1.31/1.26 inference(monotonicity,[status(thm)],[5230])).
% 1.31/1.26 tff(5232,plain,
% 1.31/1.26 (((~![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(s60, c_c2)) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | m_main_v_state2(s61, 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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2)))),
% 1.31/1.26 inference(transitivity,[status(thm)],[5231, 5229])).
% 1.31/1.26 tff(5233,plain,
% 1.31/1.26 ((~![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(s60, c_c2)) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | m_main_v_state2(s61, c_n2))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5234,plain,
% 1.31/1.26 ((~![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(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~node14(s60, s61)) | (~m_main_v_state2(s60, c_c2))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5233, 5232])).
% 1.31/1.26 tff(5235,plain,
% 1.31/1.26 (m_main_v_state2(s61, c_n2) | node9(s60) | node8(s60) | node10(s60) | node11(s60) | node12(s60) | (~m_main_v_state2(s60, c_c2))),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5234, 726, 5228])).
% 1.31/1.26 tff(5236,plain,
% 1.31/1.26 (m_main_v_state2(s61, c_n2)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5235, 5217, 5172, 5209, 5205, 5197, 5180])).
% 1.31/1.26 tff(5237,plain,
% 1.31/1.26 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_c2)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5238,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_c2)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5239,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_c2))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5238, 5237])).
% 1.31/1.26 tff(5240,plain,
% 1.31/1.26 (~m_main_v_state2(s61, c_c2)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5239, 697, 5236])).
% 1.31/1.26 tff(5241,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s61, c_c2) | (~node3(s61)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s61, c_c2) | (~node3(s61)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5242,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s61, c_c2) | (~node3(s61)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5243,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s61, c_c2) | (~node3(s61))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5242, 5241])).
% 1.31/1.26 tff(5244,plain,
% 1.31/1.26 (~node3(s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5243, 399, 5240])).
% 1.31/1.26 tff(5245,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s60, c_n1) | (~node1(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s60, c_n1) | (~node1(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5246,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s60, c_n1) | (~node1(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5247,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s60, c_n1) | (~node1(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5246, 5245])).
% 1.31/1.26 tff(5248,plain,
% 1.31/1.26 (~node1(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5247, 421, 5193])).
% 1.31/1.26 tff(5249,plain,
% 1.31/1.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s60)) | node18(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s60)) | node18(s59, s60))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5250,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s59, s60)) | node18(s59, s60))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5251,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s59, s60)) | node18(s59, s60)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5250, 5249])).
% 1.31/1.26 tff(5252,plain,
% 1.31/1.26 (node18(s59, s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5251, 125, 5163])).
% 1.31/1.26 tff(5253,plain,
% 1.31/1.26 (((~![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, s60)) | m_main_v_turn(s60, 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, s60)) | m_main_v_turn(s60, c_2))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5254,plain,
% 1.31/1.26 ((~![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, s60)) | m_main_v_turn(s60, c_2))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5255,plain,
% 1.31/1.26 ((~![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, s60)) | m_main_v_turn(s60, c_2)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5254, 5253])).
% 1.31/1.26 tff(5256,plain,
% 1.31/1.26 ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state2(s59, c_t2)) | m_main_v_turn(s60, c_2)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5255, 760, 5252])).
% 1.31/1.26 tff(5257,plain,
% 1.31/1.26 (m_main_v_turn(s60, c_2)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5256, 5116, 5152])).
% 1.31/1.26 tff(5258,plain,
% 1.31/1.26 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s60, c_1)) | (~m_main_v_turn(s60, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s60, c_1)) | (~m_main_v_turn(s60, c_2)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5259,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s60, c_1)) | (~m_main_v_turn(s60, c_2)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5260,plain,
% 1.31/1.26 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s60, c_1)) | (~m_main_v_turn(s60, c_2))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5259, 5258])).
% 1.31/1.26 tff(5261,plain,
% 1.31/1.26 (~m_main_v_turn(s60, c_1)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5260, 156, 5257])).
% 1.31/1.26 tff(5262,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s60, c_1) | (~node5(s60)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s60, c_1) | (~node5(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5263,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s60, c_1) | (~node5(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5264,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s60, c_1) | (~node5(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 1.31/1.26 tff(5265,plain,
% 1.31/1.26 (~node5(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5264, 776, 5261])).
% 1.31/1.26 tff(5266,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s60, c_n1) | (~node2(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s60, c_n1) | (~node2(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5267,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s60, c_n1) | (~node2(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5268,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s60, c_n1) | (~node2(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5267, 5266])).
% 1.31/1.26 tff(5269,plain,
% 1.31/1.26 (~node2(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5268, 787, 5193])).
% 1.31/1.26 tff(5270,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s60, c_n1) | (~node3(s60)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s60, c_n1) | (~node3(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5271,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s60, c_n1) | (~node3(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5272,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s60, c_n1) | (~node3(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5271, 5270])).
% 1.31/1.26 tff(5273,plain,
% 1.31/1.26 (~node3(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5272, 798, 5193])).
% 1.31/1.26 tff(5274,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s60, c_n2) | (~node4(s60)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s60, c_n2) | (~node4(s60)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5275,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s60, c_n2) | (~node4(s60)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5276,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s60, c_n2) | (~node4(s60))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5275, 5274])).
% 1.31/1.26 tff(5277,plain,
% 1.31/1.26 (~node4(s60)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5276, 388, 5213])).
% 1.31/1.26 tff(5278,plain,
% 1.31/1.26 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s60, s61)) | node7(s60, s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s60, s61)) | node7(s60, s61))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5279,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s60, s61)) | node7(s60, s61))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5280,plain,
% 1.31/1.26 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s60, s61)) | node7(s60, s61)),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5279, 5278])).
% 1.31/1.26 tff(5281,plain,
% 1.31/1.26 (node7(s60, s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5280, 206, 5224])).
% 1.31/1.26 tff(5282,plain,
% 1.31/1.26 (((~![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(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61) | (~node7(s60, s61)))) <=> ((~![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(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61) | (~node7(s60, s61)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5283,plain,
% 1.31/1.26 ((~![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(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61) | (~node7(s60, s61)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5284,plain,
% 1.31/1.26 ((~![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(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61) | (~node7(s60, s61))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 1.31/1.26 tff(5285,plain,
% 1.31/1.26 (m_main_v_state1(s60, c_c1) | node1(s60) | node2(s60) | node3(s60) | node4(s60) | node5(s60) | node6(s60, s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5284, 820, 5281])).
% 1.31/1.26 tff(5286,plain,
% 1.31/1.26 (node6(s60, s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5285, 5277, 5201, 5273, 5269, 5265, 5248])).
% 1.31/1.26 tff(5287,plain,
% 1.31/1.26 (((~![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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61)))) <=> ((~![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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5288,plain,
% 1.31/1.26 (((~node6(s60, s61)) | m_main_v_state1(s60, c_n1) | (~m_main_v_state1(s61, c_n1))) <=> (m_main_v_state1(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5289,plain,
% 1.31/1.26 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s60, s61)) | m_main_v_state1(s60, c_n1) | (~m_main_v_state1(s61, 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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61))))),
% 1.31/1.26 inference(monotonicity,[status(thm)],[5288])).
% 1.31/1.26 tff(5290,plain,
% 1.31/1.26 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s60, s61)) | m_main_v_state1(s60, c_n1) | (~m_main_v_state1(s61, 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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61)))),
% 1.31/1.26 inference(transitivity,[status(thm)],[5289, 5287])).
% 1.31/1.26 tff(5291,plain,
% 1.31/1.26 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s60, s61)) | m_main_v_state1(s60, c_n1) | (~m_main_v_state1(s61, c_n1)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5292,plain,
% 1.31/1.26 ((~![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(s60, c_n1) | (~m_main_v_state1(s61, c_n1)) | (~node6(s60, s61))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5291, 5290])).
% 1.31/1.26 tff(5293,plain,
% 1.31/1.26 (~m_main_v_state1(s61, c_n1)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5292, 835, 5193, 5286])).
% 1.31/1.26 tff(5294,plain,
% 1.31/1.26 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s61, c_n1) | (~node2(s61)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s61, c_n1) | (~node2(s61)))),
% 1.31/1.26 inference(rewrite,[status(thm)],[])).
% 1.31/1.26 tff(5295,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s61, c_n1) | (~node2(s61)))),
% 1.31/1.26 inference(quant_inst,[status(thm)],[])).
% 1.31/1.26 tff(5296,plain,
% 1.31/1.26 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s61, c_n1) | (~node2(s61))),
% 1.31/1.26 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 1.31/1.26 tff(5297,plain,
% 1.31/1.26 (~node2(s61)),
% 1.31/1.26 inference(unit_resolution,[status(thm)],[5296, 787, 5293])).
% 1.31/1.26 tff(5298,plain,
% 1.31/1.26 (((~![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(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61)))) <=> ((~![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(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5299,plain,
% 1.31/1.27 (((~node6(s60, s61)) | (~m_main_v_state1(s60, c_t1)) | m_main_v_state1(s61, c_t1)) <=> ((~m_main_v_state1(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5300,plain,
% 1.31/1.27 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s60, s61)) | (~m_main_v_state1(s60, c_t1)) | m_main_v_state1(s61, 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(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61))))),
% 1.31/1.27 inference(monotonicity,[status(thm)],[5299])).
% 1.31/1.27 tff(5301,plain,
% 1.31/1.27 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s60, s61)) | (~m_main_v_state1(s60, c_t1)) | m_main_v_state1(s61, 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(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61)))),
% 1.31/1.27 inference(transitivity,[status(thm)],[5300, 5298])).
% 1.31/1.27 tff(5302,plain,
% 1.31/1.27 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s60, s61)) | (~m_main_v_state1(s60, c_t1)) | m_main_v_state1(s61, c_t1))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5303,plain,
% 1.31/1.27 ((~![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(s60, c_t1)) | m_main_v_state1(s61, c_t1) | (~node6(s60, s61))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5302, 5301])).
% 1.31/1.27 tff(5304,plain,
% 1.31/1.27 (m_main_v_state1(s61, c_t1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5303, 856, 5189, 5286])).
% 1.31/1.27 tff(5305,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_t2)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5306,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_t2)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5307,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s61, c_n2)) | (~m_main_v_state2(s61, c_t2))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5306, 5305])).
% 1.31/1.27 tff(5308,plain,
% 1.31/1.27 (~m_main_v_state2(s61, c_t2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5307, 77, 5236])).
% 1.31/1.27 tff(5309,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s61, c_t2) | (~node1(s61)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s61, c_t2) | (~node1(s61)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5310,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s61, c_t2) | (~node1(s61)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5311,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s61, c_t2) | (~node1(s61))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5310, 5309])).
% 1.31/1.27 tff(5312,plain,
% 1.31/1.27 (~node1(s61)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5311, 195, 5308])).
% 1.31/1.27 tff(5313,plain,
% 1.31/1.27 (succ(s61, s62) <=> succ(s61, s62)),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5314,axiom,(succ(s61, s62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound62')).
% 1.31/1.27 tff(5315,plain,
% 1.31/1.27 (succ(s61, s62)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5314, 5313])).
% 1.31/1.27 tff(5316,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5317,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5318,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5317, 5316])).
% 1.31/1.27 tff(5319,plain,
% 1.31/1.27 (trans(s61, s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5318, 5315, 39])).
% 1.31/1.27 tff(5320,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s61, s62)) | node7(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s61, s62)) | node7(s61, s62))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5321,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s61, s62)) | node7(s61, s62))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5322,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s61, s62)) | node7(s61, s62)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5321, 5320])).
% 1.31/1.27 tff(5323,plain,
% 1.31/1.27 (node7(s61, s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5322, 206, 5319])).
% 1.31/1.27 tff(5324,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)))) <=> ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5325,plain,
% 1.31/1.27 (((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)) | m_main_v_state1(s62, c_c1)) <=> ((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5326,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)) | m_main_v_state1(s62, 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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62))))),
% 1.31/1.27 inference(monotonicity,[status(thm)],[5325])).
% 1.31/1.27 tff(5327,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)) | m_main_v_state1(s62, 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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)))),
% 1.31/1.27 inference(transitivity,[status(thm)],[5326, 5324])).
% 1.31/1.27 tff(5328,plain,
% 1.31/1.27 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62)) | m_main_v_state1(s62, c_c1))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5329,plain,
% 1.31/1.27 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61) | (~node7(s61, s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.31/1.27 tff(5330,plain,
% 1.31/1.27 ((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state1(s62, c_c1) | node1(s61) | node2(s61) | node3(s61)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5329, 892, 5323])).
% 1.31/1.27 tff(5331,plain,
% 1.31/1.27 (m_main_v_state1(s62, c_c1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5330, 5312, 5236, 5304, 5297, 5244])).
% 1.31/1.27 tff(5332,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s62, c_t1)) | (~m_main_v_state1(s62, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s62, c_t1)) | (~m_main_v_state1(s62, c_c1)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5333,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s62, c_t1)) | (~m_main_v_state1(s62, c_c1)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5334,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s62, c_t1)) | (~m_main_v_state1(s62, c_c1))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5333, 5332])).
% 1.31/1.27 tff(5335,plain,
% 1.31/1.27 (~m_main_v_state1(s62, c_t1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5334, 539, 5331])).
% 1.31/1.27 tff(5336,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s62, c_t1) | (~node5(s62)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s62, c_t1) | (~node5(s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5337,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s62, c_t1) | (~node5(s62)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5338,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s62, c_t1) | (~node5(s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5337, 5336])).
% 1.31/1.27 tff(5339,plain,
% 1.31/1.27 (~node5(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5338, 550, 5335])).
% 1.31/1.27 tff(5340,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s61, s62)) | node14(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s61, s62)) | node14(s61, s62))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5341,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s61, s62)) | node14(s61, s62))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5342,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s61, s62)) | node14(s61, s62)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5341, 5340])).
% 1.31/1.27 tff(5343,plain,
% 1.31/1.27 (node14(s61, s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5342, 7, 5319])).
% 1.31/1.27 tff(5344,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, 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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, c_t2))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5345,plain,
% 1.31/1.27 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, c_t2))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5346,plain,
% 1.31/1.27 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | (~node14(s61, s62)) | m_main_v_state2(s62, c_t2)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5345, 5344])).
% 1.31/1.27 tff(5347,plain,
% 1.31/1.27 ((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_state2(s62, c_t2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5346, 922, 5343])).
% 1.31/1.27 tff(5348,plain,
% 1.31/1.27 (m_main_v_state2(s62, c_t2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5347, 5304, 5236])).
% 1.31/1.27 tff(5349,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s62, c_n2)) | (~m_main_v_state2(s62, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s62, c_n2)) | (~m_main_v_state2(s62, c_t2)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5350,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s62, c_n2)) | (~m_main_v_state2(s62, c_t2)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5351,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s62, c_n2)) | (~m_main_v_state2(s62, c_t2))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.31/1.27 tff(5352,plain,
% 1.31/1.27 (~m_main_v_state2(s62, c_n2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5351, 77, 5348])).
% 1.31/1.27 tff(5353,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s62, c_n2) | (~node4(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s62, c_n2) | (~node4(s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5354,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s62, c_n2) | (~node4(s62)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5355,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s62, c_n2) | (~node4(s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5354, 5353])).
% 1.31/1.27 tff(5356,plain,
% 1.31/1.27 (~node4(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5355, 388, 5352])).
% 1.31/1.27 tff(5357,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s62, c_t2)) | (~m_main_v_state2(s62, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s62, c_t2)) | (~m_main_v_state2(s62, c_c2)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5358,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s62, c_t2)) | (~m_main_v_state2(s62, c_c2)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5359,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s62, c_t2)) | (~m_main_v_state2(s62, c_c2))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5358, 5357])).
% 1.31/1.27 tff(5360,plain,
% 1.31/1.27 (~m_main_v_state2(s62, c_c2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5359, 260, 5348])).
% 1.31/1.27 tff(5361,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s62, c_c2) | (~node3(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s62, c_c2) | (~node3(s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5362,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s62, c_c2) | (~node3(s62)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5363,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s62, c_c2) | (~node3(s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5362, 5361])).
% 1.31/1.27 tff(5364,plain,
% 1.31/1.27 (~node3(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5363, 399, 5360])).
% 1.31/1.27 tff(5365,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s62, c_n2) | (~node2(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s62, c_n2) | (~node2(s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5366,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s62, c_n2) | (~node2(s62)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5367,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s62, c_n2) | (~node2(s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5366, 5365])).
% 1.31/1.27 tff(5368,plain,
% 1.31/1.27 (~node2(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5367, 410, 5352])).
% 1.31/1.27 tff(5369,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s62, c_n1)) | (~m_main_v_state1(s62, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s62, c_n1)) | (~m_main_v_state1(s62, c_c1)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5370,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s62, c_n1)) | (~m_main_v_state1(s62, c_c1)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5371,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s62, c_n1)) | (~m_main_v_state1(s62, c_c1))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5370, 5369])).
% 1.31/1.27 tff(5372,plain,
% 1.31/1.27 (~m_main_v_state1(s62, c_n1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5371, 454, 5331])).
% 1.31/1.27 tff(5373,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s62, c_n1) | (~node1(s62)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s62, c_n1) | (~node1(s62)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5374,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s62, c_n1) | (~node1(s62)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5375,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s62, c_n1) | (~node1(s62))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 1.31/1.27 tff(5376,plain,
% 1.31/1.27 (~node1(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5375, 421, 5372])).
% 1.31/1.27 tff(5377,plain,
% 1.31/1.27 (succ(s62, s63) <=> succ(s62, s63)),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5378,axiom,(succ(s62, s63)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound63')).
% 1.31/1.27 tff(5379,plain,
% 1.31/1.27 (succ(s62, s63)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 1.31/1.27 tff(5380,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5381,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5382,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5381, 5380])).
% 1.31/1.27 tff(5383,plain,
% 1.31/1.27 (trans(s62, s63)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5382, 5379, 39])).
% 1.31/1.27 tff(5384,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s62, s63)) | node7(s62, s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s62, s63)) | node7(s62, s63))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5385,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s62, s63)) | node7(s62, s63))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5386,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s62, s63)) | node7(s62, s63)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5385, 5384])).
% 1.31/1.27 tff(5387,plain,
% 1.31/1.27 (node7(s62, s63)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5386, 206, 5383])).
% 1.31/1.27 tff(5388,plain,
% 1.31/1.27 (((~![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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)))) <=> ((~![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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5389,plain,
% 1.31/1.27 (((~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)) | m_main_v_state1(s63, c_n1)) <=> (m_main_v_state1(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5390,plain,
% 1.31/1.27 (((~![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(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)) | m_main_v_state1(s63, 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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63))))),
% 1.31/1.27 inference(monotonicity,[status(thm)],[5389])).
% 1.31/1.27 tff(5391,plain,
% 1.31/1.27 (((~![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(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)) | m_main_v_state1(s63, 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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)))),
% 1.31/1.27 inference(transitivity,[status(thm)],[5390, 5388])).
% 1.31/1.27 tff(5392,plain,
% 1.31/1.27 ((~![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(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63)) | m_main_v_state1(s63, c_n1))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5393,plain,
% 1.31/1.27 ((~![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(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62) | (~node7(s62, s63))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5392, 5391])).
% 1.31/1.27 tff(5394,plain,
% 1.31/1.27 (m_main_v_state1(s63, c_n1) | (~m_main_v_state1(s62, c_c1)) | node1(s62) | node2(s62) | node3(s62) | node4(s62) | node5(s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5393, 584, 5387])).
% 1.31/1.27 tff(5395,plain,
% 1.31/1.27 (m_main_v_state1(s63, c_n1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5394, 5376, 5331, 5368, 5364, 5356, 5339])).
% 1.31/1.27 tff(5396,plain,
% 1.31/1.27 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s61, c_t2) | (~node15(s61)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s61, c_t2) | (~node15(s61)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5397,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s61, c_t2) | (~node15(s61)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5398,plain,
% 1.31/1.27 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s61, c_t2) | (~node15(s61))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5397, 5396])).
% 1.31/1.27 tff(5399,plain,
% 1.31/1.27 (~node15(s61)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5398, 103, 5308])).
% 1.31/1.27 tff(5400,plain,
% 1.31/1.27 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s61, s62)) | node18(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s61, s62)) | node18(s61, s62))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5401,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s61, s62)) | node18(s61, s62))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5402,plain,
% 1.31/1.27 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s61, s62)) | node18(s61, s62)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5401, 5400])).
% 1.31/1.27 tff(5403,plain,
% 1.31/1.27 (node18(s61, s62)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5402, 125, 5319])).
% 1.31/1.27 tff(5404,plain,
% 1.31/1.27 (((~![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(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, 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(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5405,plain,
% 1.31/1.27 (((~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node15(s61) | (~node18(s61, s62)) | m_main_v_turn(s62, c_1)) <=> (node15(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5406,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node15(s61) | (~node18(s61, s62)) | m_main_v_turn(s62, 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(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1)))),
% 1.31/1.27 inference(monotonicity,[status(thm)],[5405])).
% 1.31/1.27 tff(5407,plain,
% 1.31/1.27 (((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node15(s61) | (~node18(s61, s62)) | m_main_v_turn(s62, 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(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1))),
% 1.31/1.27 inference(transitivity,[status(thm)],[5406, 5404])).
% 1.31/1.27 tff(5408,plain,
% 1.31/1.27 ((~![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(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | node15(s61) | (~node18(s61, s62)) | m_main_v_turn(s62, c_1))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5409,plain,
% 1.31/1.27 ((~![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(s61) | (~node18(s61, s62)) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1)),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5408, 5407])).
% 1.31/1.27 tff(5410,plain,
% 1.31/1.27 (node15(s61) | (~m_main_v_state1(s61, c_t1)) | (~m_main_v_state2(s61, c_n2)) | m_main_v_turn(s62, c_1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5409, 992, 5403])).
% 1.31/1.27 tff(5411,plain,
% 1.31/1.27 (m_main_v_turn(s62, c_1)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5410, 5399, 5236, 5304])).
% 1.31/1.27 tff(5412,plain,
% 1.31/1.27 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s62, c_1)) | (~m_main_v_turn(s62, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s62, c_1)) | (~m_main_v_turn(s62, c_2)))),
% 1.31/1.27 inference(rewrite,[status(thm)],[])).
% 1.31/1.27 tff(5413,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s62, c_1)) | (~m_main_v_turn(s62, c_2)))),
% 1.31/1.27 inference(quant_inst,[status(thm)],[])).
% 1.31/1.27 tff(5414,plain,
% 1.31/1.27 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s62, c_1)) | (~m_main_v_turn(s62, c_2))),
% 1.31/1.27 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 1.31/1.27 tff(5415,plain,
% 1.31/1.27 (~m_main_v_turn(s62, c_2)),
% 1.31/1.27 inference(unit_resolution,[status(thm)],[5414, 156, 5411])).
% 1.31/1.28 tff(5416,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s62, c_2) | (~node12(s62)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s62, c_2) | (~node12(s62)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5417,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s62, c_2) | (~node12(s62)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5418,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s62, c_2) | (~node12(s62))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5417, 5416])).
% 1.31/1.28 tff(5419,plain,
% 1.31/1.28 (~node12(s62)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5418, 184, 5415])).
% 1.31/1.28 tff(5420,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s62, c_n2) | (~node8(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s62, c_n2) | (~node8(s62)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5421,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s62, c_n2) | (~node8(s62)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5422,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s62, c_n2) | (~node8(s62))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5421, 5420])).
% 1.31/1.28 tff(5423,plain,
% 1.31/1.28 (~node8(s62)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5422, 271, 5352])).
% 1.31/1.28 tff(5424,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s62, c_n2) | (~node9(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s62, c_n2) | (~node9(s62)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5425,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s62, c_n2) | (~node9(s62)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5426,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s62, c_n2) | (~node9(s62))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5425, 5424])).
% 1.31/1.28 tff(5427,plain,
% 1.31/1.28 (~node9(s62)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5426, 88, 5352])).
% 1.31/1.28 tff(5428,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s62, c_n2) | (~node10(s62)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s62, c_n2) | (~node10(s62)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5429,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s62, c_n2) | (~node10(s62)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5430,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s62, c_n2) | (~node10(s62))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5429, 5428])).
% 1.31/1.28 tff(5431,plain,
% 1.31/1.28 (~node10(s62)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5430, 249, 5352])).
% 1.31/1.28 tff(5432,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s62, c_n1) | (~node11(s62)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s62, c_n1) | (~node11(s62)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5433,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s62, c_n1) | (~node11(s62)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5434,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s62, c_n1) | (~node11(s62))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 1.31/1.28 tff(5435,plain,
% 1.31/1.28 (~node11(s62)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5434, 238, 5372])).
% 1.31/1.28 tff(5436,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s62, s63)) | node14(s62, s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s62, s63)) | node14(s62, s63))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5437,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s62, s63)) | node14(s62, s63))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5438,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s62, s63)) | node14(s62, s63)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5437, 5436])).
% 1.31/1.28 tff(5439,plain,
% 1.31/1.28 (node14(s62, s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5438, 7, 5383])).
% 1.31/1.28 tff(5440,plain,
% 1.31/1.28 (((~![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(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63) | (~node14(s62, s63)))) <=> ((~![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(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63) | (~node14(s62, s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5441,plain,
% 1.31/1.28 ((~![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(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63) | (~node14(s62, s63)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5442,plain,
% 1.31/1.28 ((~![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(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63) | (~node14(s62, s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5441, 5440])).
% 1.31/1.28 tff(5443,plain,
% 1.31/1.28 (m_main_v_state2(s62, c_c2) | node9(s62) | node8(s62) | node10(s62) | node11(s62) | node12(s62) | node13(s62, s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5442, 296, 5439])).
% 1.31/1.28 tff(5444,plain,
% 1.31/1.28 (node13(s62, s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5443, 5435, 5360, 5431, 5427, 5423, 5419])).
% 1.31/1.28 tff(5445,plain,
% 1.31/1.28 (((~![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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63)))) <=> ((~![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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5446,plain,
% 1.31/1.28 (((~node13(s62, s63)) | (~m_main_v_state2(s62, c_t2)) | m_main_v_state2(s63, c_t2)) <=> ((~m_main_v_state2(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5447,plain,
% 1.31/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s62, s63)) | (~m_main_v_state2(s62, c_t2)) | m_main_v_state2(s63, 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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63))))),
% 1.31/1.28 inference(monotonicity,[status(thm)],[5446])).
% 1.31/1.28 tff(5448,plain,
% 1.31/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s62, s63)) | (~m_main_v_state2(s62, c_t2)) | m_main_v_state2(s63, 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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63)))),
% 1.31/1.28 inference(transitivity,[status(thm)],[5447, 5445])).
% 1.31/1.28 tff(5449,plain,
% 1.31/1.28 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s62, s63)) | (~m_main_v_state2(s62, c_t2)) | m_main_v_state2(s63, c_t2))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5450,plain,
% 1.31/1.28 ((~![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(s62, c_t2)) | m_main_v_state2(s63, c_t2) | (~node13(s62, s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 1.31/1.28 tff(5451,plain,
% 1.31/1.28 (m_main_v_state2(s63, c_t2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5450, 518, 5348, 5444])).
% 1.31/1.28 tff(5452,plain,
% 1.31/1.28 (succ(s63, s64) <=> succ(s63, s64)),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5453,axiom,(succ(s63, s64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound64')).
% 1.31/1.28 tff(5454,plain,
% 1.31/1.28 (succ(s63, s64)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 1.31/1.28 tff(5455,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5456,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5457,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 1.31/1.28 tff(5458,plain,
% 1.31/1.28 (trans(s63, s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5457, 5454, 39])).
% 1.31/1.28 tff(5459,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s63, s64)) | node7(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s63, s64)) | node7(s63, s64))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5460,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s63, s64)) | node7(s63, s64))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5461,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s63, s64)) | node7(s63, s64)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5460, 5459])).
% 1.31/1.28 tff(5462,plain,
% 1.31/1.28 (node7(s63, s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5461, 206, 5458])).
% 1.31/1.28 tff(5463,plain,
% 1.31/1.28 (((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, 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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, c_t1))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5464,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, c_t1))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5465,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node7(s63, s64)) | m_main_v_state1(s64, c_t1)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5464, 5463])).
% 1.31/1.28 tff(5466,plain,
% 1.31/1.28 ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | m_main_v_state1(s64, c_t1)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5465, 651, 5462])).
% 1.31/1.28 tff(5467,plain,
% 1.31/1.28 (m_main_v_state1(s64, c_t1)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5466, 5451, 5395])).
% 1.31/1.28 tff(5468,plain,
% 1.31/1.28 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s64, c_n1)) | (~m_main_v_state1(s64, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s64, c_n1)) | (~m_main_v_state1(s64, c_t1)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5469,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s64, c_n1)) | (~m_main_v_state1(s64, c_t1)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5470,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s64, c_n1)) | (~m_main_v_state1(s64, c_t1))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5469, 5468])).
% 1.31/1.28 tff(5471,plain,
% 1.31/1.28 (~m_main_v_state1(s64, c_n1)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5470, 17, 5467])).
% 1.31/1.28 tff(5472,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s64, c_n1) | (~node1(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s64, c_n1) | (~node1(s64)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5473,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s64, c_n1) | (~node1(s64)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5474,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s64, c_n1) | (~node1(s64))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 1.31/1.28 tff(5475,plain,
% 1.31/1.28 (~node1(s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5474, 421, 5471])).
% 1.31/1.28 tff(5476,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s63, s64)) | node18(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s63, s64)) | node18(s63, s64))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5477,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s63, s64)) | node18(s63, s64))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5478,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s63, s64)) | node18(s63, s64)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5477, 5476])).
% 1.31/1.28 tff(5479,plain,
% 1.31/1.28 (node18(s63, s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5478, 125, 5458])).
% 1.31/1.28 tff(5480,plain,
% 1.31/1.28 (((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, 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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, c_2))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5481,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, c_2))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5482,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | (~node18(s63, s64)) | m_main_v_turn(s64, c_2)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5481, 5480])).
% 1.31/1.28 tff(5483,plain,
% 1.31/1.28 ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | m_main_v_turn(s64, c_2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5482, 760, 5479])).
% 1.31/1.28 tff(5484,plain,
% 1.31/1.28 (m_main_v_turn(s64, c_2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5483, 5451, 5395])).
% 1.31/1.28 tff(5485,plain,
% 1.31/1.28 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s64, c_1)) | (~m_main_v_turn(s64, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s64, c_1)) | (~m_main_v_turn(s64, c_2)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5486,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s64, c_1)) | (~m_main_v_turn(s64, c_2)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5487,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s64, c_1)) | (~m_main_v_turn(s64, c_2))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5486, 5485])).
% 1.31/1.28 tff(5488,plain,
% 1.31/1.28 (~m_main_v_turn(s64, c_1)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5487, 156, 5484])).
% 1.31/1.28 tff(5489,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s64, c_1) | (~node5(s64)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s64, c_1) | (~node5(s64)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5490,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s64, c_1) | (~node5(s64)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5491,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s64, c_1) | (~node5(s64))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5490, 5489])).
% 1.31/1.28 tff(5492,plain,
% 1.31/1.28 (~node5(s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5491, 776, 5488])).
% 1.31/1.28 tff(5493,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s64, c_n1) | (~node2(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s64, c_n1) | (~node2(s64)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5494,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s64, c_n1) | (~node2(s64)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5495,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s64, c_n1) | (~node2(s64))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 1.31/1.28 tff(5496,plain,
% 1.31/1.28 (~node2(s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5495, 787, 5471])).
% 1.31/1.28 tff(5497,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s64, c_n1) | (~node3(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s64, c_n1) | (~node3(s64)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5498,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s64, c_n1) | (~node3(s64)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5499,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s64, c_n1) | (~node3(s64))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 1.31/1.28 tff(5500,plain,
% 1.31/1.28 (~node3(s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5499, 798, 5471])).
% 1.31/1.28 tff(5501,plain,
% 1.31/1.28 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s64, c_t1)) | (~m_main_v_state1(s64, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s64, c_t1)) | (~m_main_v_state1(s64, c_c1)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5502,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s64, c_t1)) | (~m_main_v_state1(s64, c_c1)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5503,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s64, c_t1)) | (~m_main_v_state1(s64, c_c1))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5502, 5501])).
% 1.31/1.28 tff(5504,plain,
% 1.31/1.28 (~m_main_v_state1(s64, c_c1)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5503, 539, 5467])).
% 1.31/1.28 tff(5505,plain,
% 1.31/1.28 (((~![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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63)))) <=> ((~![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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5506,plain,
% 1.31/1.28 (((~node13(s62, s63)) | m_main_v_state2(s62, c_n2) | (~m_main_v_state2(s63, c_n2))) <=> (m_main_v_state2(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5507,plain,
% 1.31/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s62, s63)) | m_main_v_state2(s62, c_n2) | (~m_main_v_state2(s63, 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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63))))),
% 1.31/1.28 inference(monotonicity,[status(thm)],[5506])).
% 1.31/1.28 tff(5508,plain,
% 1.31/1.28 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s62, s63)) | m_main_v_state2(s62, c_n2) | (~m_main_v_state2(s63, 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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63)))),
% 1.31/1.28 inference(transitivity,[status(thm)],[5507, 5505])).
% 1.31/1.28 tff(5509,plain,
% 1.31/1.28 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s62, s63)) | m_main_v_state2(s62, c_n2) | (~m_main_v_state2(s63, c_n2)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5510,plain,
% 1.31/1.28 ((~![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(s62, c_n2) | (~m_main_v_state2(s63, c_n2)) | (~node13(s62, s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 1.31/1.28 tff(5511,plain,
% 1.31/1.28 (~m_main_v_state2(s63, c_n2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5510, 311, 5352, 5444])).
% 1.31/1.28 tff(5512,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s63, c_n2) | (~node9(s63)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s63, c_n2) | (~node9(s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5513,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s63, c_n2) | (~node9(s63)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5514,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s63, c_n2) | (~node9(s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 1.31/1.28 tff(5515,plain,
% 1.31/1.28 (~node9(s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5514, 88, 5511])).
% 1.31/1.28 tff(5516,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s63, c_n2) | (~node10(s63)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s63, c_n2) | (~node10(s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5517,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s63, c_n2) | (~node10(s63)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5518,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s63, c_n2) | (~node10(s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5517, 5516])).
% 1.31/1.28 tff(5519,plain,
% 1.31/1.28 (~node10(s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5518, 249, 5511])).
% 1.31/1.28 tff(5520,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s63, c_n2) | (~node8(s63)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s63, c_n2) | (~node8(s63)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5521,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s63, c_n2) | (~node8(s63)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5522,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s63, c_n2) | (~node8(s63))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5521, 5520])).
% 1.31/1.28 tff(5523,plain,
% 1.31/1.28 (~node8(s63)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5522, 271, 5511])).
% 1.31/1.28 tff(5524,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s63, s64)) | node14(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s63, s64)) | node14(s63, s64))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5525,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s63, s64)) | node14(s63, s64))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5526,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s63, s64)) | node14(s63, s64)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5525, 5524])).
% 1.31/1.28 tff(5527,plain,
% 1.31/1.28 (node14(s63, s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5526, 7, 5458])).
% 1.31/1.28 tff(5528,plain,
% 1.31/1.28 (((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | node9(s63) | node8(s63) | node10(s63) | (~node14(s63, s64)) | m_main_v_state2(s64, 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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | node9(s63) | node8(s63) | node10(s63) | (~node14(s63, s64)) | m_main_v_state2(s64, c_c2))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5529,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | node9(s63) | node8(s63) | node10(s63) | (~node14(s63, s64)) | m_main_v_state2(s64, c_c2))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5530,plain,
% 1.31/1.28 ((~![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(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | node9(s63) | node8(s63) | node10(s63) | (~node14(s63, s64)) | m_main_v_state2(s64, c_c2)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5529, 5528])).
% 1.31/1.28 tff(5531,plain,
% 1.31/1.28 ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state2(s63, c_t2)) | node9(s63) | node8(s63) | node10(s63) | m_main_v_state2(s64, c_c2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5530, 617, 5527])).
% 1.31/1.28 tff(5532,plain,
% 1.31/1.28 (m_main_v_state2(s64, c_c2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5531, 5523, 5395, 5451, 5519, 5515])).
% 1.31/1.28 tff(5533,plain,
% 1.31/1.28 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s64, c_n2)) | (~m_main_v_state2(s64, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s64, c_n2)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5534,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s64, c_n2)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5535,plain,
% 1.31/1.28 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s64, c_n2)) | (~m_main_v_state2(s64, c_c2))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5534, 5533])).
% 1.31/1.28 tff(5536,plain,
% 1.31/1.28 (~m_main_v_state2(s64, c_n2)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5535, 697, 5532])).
% 1.31/1.28 tff(5537,plain,
% 1.31/1.28 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s64, c_n2) | (~node4(s64)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s64, c_n2) | (~node4(s64)))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5538,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s64, c_n2) | (~node4(s64)))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5539,plain,
% 1.31/1.28 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s64, c_n2) | (~node4(s64))),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 1.31/1.28 tff(5540,plain,
% 1.31/1.28 (~node4(s64)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5539, 388, 5536])).
% 1.31/1.28 tff(5541,plain,
% 1.31/1.28 (succ(s64, s65) <=> succ(s64, s65)),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5542,axiom,(succ(s64, s65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound65')).
% 1.31/1.28 tff(5543,plain,
% 1.31/1.28 (succ(s64, s65)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5542, 5541])).
% 1.31/1.28 tff(5544,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65))),
% 1.31/1.28 inference(rewrite,[status(thm)],[])).
% 1.31/1.28 tff(5545,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))),
% 1.31/1.28 inference(quant_inst,[status(thm)],[])).
% 1.31/1.28 tff(5546,plain,
% 1.31/1.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65)),
% 1.31/1.28 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 1.31/1.28 tff(5547,plain,
% 1.31/1.28 (trans(s64, s65)),
% 1.31/1.28 inference(unit_resolution,[status(thm)],[5546, 5543, 39])).
% 1.31/1.28 tff(5548,plain,
% 1.31/1.28 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s64, s65)) | node7(s64, s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s64, s65)) | node7(s64, s65))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5549,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s64, s65)) | node7(s64, s65))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5550,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s64, s65)) | node7(s64, s65)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5549, 5548])).
% 1.31/1.29 tff(5551,plain,
% 1.31/1.29 (node7(s64, s65)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5550, 206, 5547])).
% 1.31/1.29 tff(5552,plain,
% 1.31/1.29 (((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65)))) <=> ((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5553,plain,
% 1.31/1.29 ((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5554,plain,
% 1.31/1.29 ((~![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(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65) | (~node7(s64, s65))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5553, 5552])).
% 1.31/1.29 tff(5555,plain,
% 1.31/1.29 (m_main_v_state1(s64, c_c1) | node1(s64) | node2(s64) | node3(s64) | node4(s64) | node5(s64) | node6(s64, s65)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5554, 820, 5551])).
% 1.31/1.29 tff(5556,plain,
% 1.31/1.29 (node6(s64, s65)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5555, 5540, 5504, 5500, 5496, 5492, 5475])).
% 1.31/1.29 tff(5557,plain,
% 1.31/1.29 (((~![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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65)))) <=> ((~![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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5558,plain,
% 1.31/1.29 (((~node6(s64, s65)) | (~m_main_v_state1(s64, c_t1)) | m_main_v_state1(s65, c_t1)) <=> ((~m_main_v_state1(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5559,plain,
% 1.31/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s64, s65)) | (~m_main_v_state1(s64, c_t1)) | m_main_v_state1(s65, 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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65))))),
% 1.31/1.29 inference(monotonicity,[status(thm)],[5558])).
% 1.31/1.29 tff(5560,plain,
% 1.31/1.29 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s64, s65)) | (~m_main_v_state1(s64, c_t1)) | m_main_v_state1(s65, 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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65)))),
% 1.31/1.29 inference(transitivity,[status(thm)],[5559, 5557])).
% 1.31/1.29 tff(5561,plain,
% 1.31/1.29 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s64, s65)) | (~m_main_v_state1(s64, c_t1)) | m_main_v_state1(s65, c_t1))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5562,plain,
% 1.31/1.29 ((~![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(s64, c_t1)) | m_main_v_state1(s65, c_t1) | (~node6(s64, s65))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5561, 5560])).
% 1.31/1.29 tff(5563,plain,
% 1.31/1.29 (m_main_v_state1(s65, c_t1)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5562, 856, 5467, 5556])).
% 1.31/1.29 tff(5564,plain,
% 1.31/1.29 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s64, c_t2)) | (~m_main_v_state2(s64, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s64, c_t2)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5565,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s64, c_t2)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5566,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s64, c_t2)) | (~m_main_v_state2(s64, c_c2))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5565, 5564])).
% 1.31/1.29 tff(5567,plain,
% 1.31/1.29 (~m_main_v_state2(s64, c_t2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5566, 260, 5532])).
% 1.31/1.29 tff(5568,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s64, c_t2) | (~node12(s64)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s64, c_t2) | (~node12(s64)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5569,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s64, c_t2) | (~node12(s64)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5570,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s64, c_t2) | (~node12(s64))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 1.31/1.29 tff(5571,plain,
% 1.31/1.29 (~node12(s64)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5570, 633, 5567])).
% 1.31/1.29 tff(5572,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s64, c_n1) | (~node11(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s64, c_n1) | (~node11(s64)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5573,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s64, c_n1) | (~node11(s64)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5574,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s64, c_n1) | (~node11(s64))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 1.31/1.29 tff(5575,plain,
% 1.31/1.29 (~node11(s64)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5574, 238, 5471])).
% 1.31/1.29 tff(5576,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s64, c_c1) | (~node10(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s64, c_c1) | (~node10(s64)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5577,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s64, c_c1) | (~node10(s64)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5578,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s64, c_c1) | (~node10(s64))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5577, 5576])).
% 1.31/1.29 tff(5579,plain,
% 1.31/1.29 (~node10(s64)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5578, 675, 5504])).
% 1.31/1.29 tff(5580,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s64, c_n1) | (~node9(s64)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s64, c_n1) | (~node9(s64)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5581,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s64, c_n1) | (~node9(s64)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5582,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s64, c_n1) | (~node9(s64))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 1.31/1.29 tff(5583,plain,
% 1.31/1.29 (~node9(s64)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5582, 686, 5471])).
% 1.31/1.29 tff(5584,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s64, c_n2) | (~node8(s64)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s64, c_n2) | (~node8(s64)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5585,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s64, c_n2) | (~node8(s64)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5586,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s64, c_n2) | (~node8(s64))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5585, 5584])).
% 1.31/1.29 tff(5587,plain,
% 1.31/1.29 (~node8(s64)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5586, 271, 5536])).
% 1.31/1.29 tff(5588,plain,
% 1.31/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s64, s65)) | node14(s64, s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s64, s65)) | node14(s64, s65))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5589,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s64, s65)) | node14(s64, s65))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5590,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s64, s65)) | node14(s64, s65)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5589, 5588])).
% 1.31/1.29 tff(5591,plain,
% 1.31/1.29 (node14(s64, s65)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5590, 7, 5547])).
% 1.31/1.29 tff(5592,plain,
% 1.31/1.29 (((~![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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, 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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5593,plain,
% 1.31/1.29 (((~m_main_v_state2(s64, c_c2)) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | m_main_v_state2(s65, c_n2)) <=> (m_main_v_state2(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5594,plain,
% 1.31/1.29 (((~![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(s64, c_c2)) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | m_main_v_state2(s65, 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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2))))),
% 1.31/1.29 inference(monotonicity,[status(thm)],[5593])).
% 1.31/1.29 tff(5595,plain,
% 1.31/1.29 (((~![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(s64, c_c2)) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | m_main_v_state2(s65, 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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2)))),
% 1.31/1.29 inference(transitivity,[status(thm)],[5594, 5592])).
% 1.31/1.29 tff(5596,plain,
% 1.31/1.29 ((~![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(s64, c_c2)) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | m_main_v_state2(s65, c_n2))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5597,plain,
% 1.31/1.29 ((~![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(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~node14(s64, s65)) | (~m_main_v_state2(s64, c_c2))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5596, 5595])).
% 1.31/1.29 tff(5598,plain,
% 1.31/1.29 (m_main_v_state2(s65, c_n2) | node9(s64) | node8(s64) | node10(s64) | node11(s64) | node12(s64) | (~m_main_v_state2(s64, c_c2))),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5597, 726, 5591])).
% 1.31/1.29 tff(5599,plain,
% 1.31/1.29 (m_main_v_state2(s65, c_n2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5598, 5587, 5532, 5583, 5579, 5575, 5571])).
% 1.31/1.29 tff(5600,plain,
% 1.31/1.29 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_t2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5601,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_t2)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5602,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_t2))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5601, 5600])).
% 1.31/1.29 tff(5603,plain,
% 1.31/1.29 (~m_main_v_state2(s65, c_t2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5602, 77, 5599])).
% 1.31/1.29 tff(5604,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s65, c_t2) | (~node15(s65)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s65, c_t2) | (~node15(s65)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5605,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s65, c_t2) | (~node15(s65)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5606,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s65, c_t2) | (~node15(s65))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5605, 5604])).
% 1.31/1.29 tff(5607,plain,
% 1.31/1.29 (~node15(s65)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5606, 103, 5603])).
% 1.31/1.29 tff(5608,plain,
% 1.31/1.29 (succ(s65, s66) <=> succ(s65, s66)),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5609,axiom,(succ(s65, s66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound66')).
% 1.31/1.29 tff(5610,plain,
% 1.31/1.29 (succ(s65, s66)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5609, 5608])).
% 1.31/1.29 tff(5611,plain,
% 1.31/1.29 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5612,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5613,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5612, 5611])).
% 1.31/1.29 tff(5614,plain,
% 1.31/1.29 (trans(s65, s66)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5613, 5610, 39])).
% 1.31/1.29 tff(5615,plain,
% 1.31/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s65, s66)) | node18(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s65, s66)) | node18(s65, s66))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5616,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s65, s66)) | node18(s65, s66))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5617,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s65, s66)) | node18(s65, s66)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5616, 5615])).
% 1.31/1.29 tff(5618,plain,
% 1.31/1.29 (node18(s65, s66)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5617, 125, 5614])).
% 1.31/1.29 tff(5619,plain,
% 1.31/1.29 (((~![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(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, 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(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5620,plain,
% 1.31/1.29 (((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node15(s65) | (~node18(s65, s66)) | m_main_v_turn(s66, c_1)) <=> (node15(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5621,plain,
% 1.31/1.29 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node15(s65) | (~node18(s65, s66)) | m_main_v_turn(s66, 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(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1)))),
% 1.31/1.29 inference(monotonicity,[status(thm)],[5620])).
% 1.31/1.29 tff(5622,plain,
% 1.31/1.29 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node15(s65) | (~node18(s65, s66)) | m_main_v_turn(s66, 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(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1))),
% 1.31/1.29 inference(transitivity,[status(thm)],[5621, 5619])).
% 1.31/1.29 tff(5623,plain,
% 1.31/1.29 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node15(s65) | (~node18(s65, s66)) | m_main_v_turn(s66, c_1))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5624,plain,
% 1.31/1.29 ((~![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(s65) | (~node18(s65, s66)) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5623, 5622])).
% 1.31/1.29 tff(5625,plain,
% 1.31/1.29 (node15(s65) | (~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_turn(s66, c_1)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5624, 992, 5618])).
% 1.31/1.29 tff(5626,plain,
% 1.31/1.29 (m_main_v_turn(s66, c_1)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5625, 5607, 5599, 5563])).
% 1.31/1.29 tff(5627,plain,
% 1.31/1.29 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s66, c_1)) | (~m_main_v_turn(s66, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s66, c_1)) | (~m_main_v_turn(s66, c_2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5628,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s66, c_1)) | (~m_main_v_turn(s66, c_2)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5629,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s66, c_1)) | (~m_main_v_turn(s66, c_2))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 1.31/1.29 tff(5630,plain,
% 1.31/1.29 (~m_main_v_turn(s66, c_2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5629, 156, 5626])).
% 1.31/1.29 tff(5631,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s66, c_2) | (~node12(s66)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s66, c_2) | (~node12(s66)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5632,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s66, c_2) | (~node12(s66)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5633,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s66, c_2) | (~node12(s66))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5632, 5631])).
% 1.31/1.29 tff(5634,plain,
% 1.31/1.29 (~node12(s66)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5633, 184, 5630])).
% 1.31/1.29 tff(5635,plain,
% 1.31/1.29 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s65, s66)) | node14(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s65, s66)) | node14(s65, s66))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5636,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s65, s66)) | node14(s65, s66))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5637,plain,
% 1.31/1.29 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s65, s66)) | node14(s65, s66)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5636, 5635])).
% 1.31/1.29 tff(5638,plain,
% 1.31/1.29 (node14(s65, s66)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5637, 7, 5614])).
% 1.31/1.29 tff(5639,plain,
% 1.31/1.29 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | (~node14(s65, s66)) | m_main_v_state2(s66, 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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | (~node14(s65, s66)) | m_main_v_state2(s66, c_t2))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5640,plain,
% 1.31/1.29 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | (~node14(s65, s66)) | m_main_v_state2(s66, c_t2))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5641,plain,
% 1.31/1.29 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | (~node14(s65, s66)) | m_main_v_state2(s66, c_t2)),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5640, 5639])).
% 1.31/1.29 tff(5642,plain,
% 1.31/1.29 ((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state2(s66, c_t2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5641, 922, 5638])).
% 1.31/1.29 tff(5643,plain,
% 1.31/1.29 (m_main_v_state2(s66, c_t2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5642, 5563, 5599])).
% 1.31/1.29 tff(5644,plain,
% 1.31/1.29 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s66, c_n2)) | (~m_main_v_state2(s66, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s66, c_n2)) | (~m_main_v_state2(s66, c_t2)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5645,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s66, c_n2)) | (~m_main_v_state2(s66, c_t2)))),
% 1.31/1.29 inference(quant_inst,[status(thm)],[])).
% 1.31/1.29 tff(5646,plain,
% 1.31/1.29 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s66, c_n2)) | (~m_main_v_state2(s66, c_t2))),
% 1.31/1.29 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 1.31/1.29 tff(5647,plain,
% 1.31/1.29 (~m_main_v_state2(s66, c_n2)),
% 1.31/1.29 inference(unit_resolution,[status(thm)],[5646, 77, 5643])).
% 1.31/1.29 tff(5648,plain,
% 1.31/1.29 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s66, c_n2) | (~node8(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s66, c_n2) | (~node8(s66)))),
% 1.31/1.29 inference(rewrite,[status(thm)],[])).
% 1.31/1.29 tff(5649,plain,
% 1.31/1.29 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s66, c_n2) | (~node8(s66)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5650,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s66, c_n2) | (~node8(s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5649, 5648])).
% 1.31/1.30 tff(5651,plain,
% 1.31/1.30 (~node8(s66)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5650, 271, 5647])).
% 1.31/1.30 tff(5652,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s66, c_n2) | (~node9(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s66, c_n2) | (~node9(s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5653,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s66, c_n2) | (~node9(s66)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5654,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s66, c_n2) | (~node9(s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 1.31/1.30 tff(5655,plain,
% 1.31/1.30 (~node9(s66)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5654, 88, 5647])).
% 1.31/1.30 tff(5656,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s66, c_n2) | (~node10(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s66, c_n2) | (~node10(s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5657,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s66, c_n2) | (~node10(s66)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5658,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s66, c_n2) | (~node10(s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5657, 5656])).
% 1.31/1.30 tff(5659,plain,
% 1.31/1.30 (~node10(s66)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5658, 249, 5647])).
% 1.31/1.30 tff(5660,plain,
% 1.31/1.30 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s66, c_t2)) | (~m_main_v_state2(s66, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s66, c_t2)) | (~m_main_v_state2(s66, c_c2)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5661,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s66, c_t2)) | (~m_main_v_state2(s66, c_c2)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5662,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s66, c_t2)) | (~m_main_v_state2(s66, c_c2))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5661, 5660])).
% 1.31/1.30 tff(5663,plain,
% 1.31/1.30 (~m_main_v_state2(s66, c_c2)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5662, 260, 5643])).
% 1.31/1.30 tff(5664,plain,
% 1.31/1.30 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_c2)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5665,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_c2)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5666,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s65, c_n2)) | (~m_main_v_state2(s65, c_c2))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5665, 5664])).
% 1.31/1.30 tff(5667,plain,
% 1.31/1.30 (~m_main_v_state2(s65, c_c2)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5666, 697, 5599])).
% 1.31/1.30 tff(5668,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s65, c_c2) | (~node3(s65)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s65, c_c2) | (~node3(s65)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5669,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s65, c_c2) | (~node3(s65)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5670,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s65, c_c2) | (~node3(s65))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5669, 5668])).
% 1.31/1.30 tff(5671,plain,
% 1.31/1.30 (~node3(s65)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5670, 399, 5667])).
% 1.31/1.30 tff(5672,plain,
% 1.31/1.30 (((~![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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65)))) <=> ((~![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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5673,plain,
% 1.31/1.30 (((~node6(s64, s65)) | m_main_v_state1(s64, c_n1) | (~m_main_v_state1(s65, c_n1))) <=> (m_main_v_state1(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5674,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s64, s65)) | m_main_v_state1(s64, c_n1) | (~m_main_v_state1(s65, 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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65))))),
% 1.31/1.30 inference(monotonicity,[status(thm)],[5673])).
% 1.31/1.30 tff(5675,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s64, s65)) | m_main_v_state1(s64, c_n1) | (~m_main_v_state1(s65, 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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65)))),
% 1.31/1.30 inference(transitivity,[status(thm)],[5674, 5672])).
% 1.31/1.30 tff(5676,plain,
% 1.31/1.30 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s64, s65)) | m_main_v_state1(s64, c_n1) | (~m_main_v_state1(s65, c_n1)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5677,plain,
% 1.31/1.30 ((~![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(s64, c_n1) | (~m_main_v_state1(s65, c_n1)) | (~node6(s64, s65))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5676, 5675])).
% 1.31/1.30 tff(5678,plain,
% 1.31/1.30 (~m_main_v_state1(s65, c_n1)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5677, 835, 5471, 5556])).
% 1.31/1.30 tff(5679,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s65, c_n1) | (~node2(s65)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s65, c_n1) | (~node2(s65)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5680,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s65, c_n1) | (~node2(s65)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5681,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s65, c_n1) | (~node2(s65))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5680, 5679])).
% 1.31/1.30 tff(5682,plain,
% 1.31/1.30 (~node2(s65)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5681, 787, 5678])).
% 1.31/1.30 tff(5683,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s65, c_t2) | (~node1(s65)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s65, c_t2) | (~node1(s65)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5684,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s65, c_t2) | (~node1(s65)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5685,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s65, c_t2) | (~node1(s65))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5684, 5683])).
% 1.31/1.30 tff(5686,plain,
% 1.31/1.30 (~node1(s65)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5685, 195, 5603])).
% 1.31/1.30 tff(5687,plain,
% 1.31/1.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s65, s66)) | node7(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s65, s66)) | node7(s65, s66))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5688,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s65, s66)) | node7(s65, s66))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5689,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s65, s66)) | node7(s65, s66)),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 1.31/1.30 tff(5690,plain,
% 1.31/1.30 (node7(s65, s66)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5689, 206, 5614])).
% 1.31/1.30 tff(5691,plain,
% 1.31/1.30 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)))) <=> ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5692,plain,
% 1.31/1.30 (((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)) | m_main_v_state1(s66, c_c1)) <=> ((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5693,plain,
% 1.31/1.30 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)) | m_main_v_state1(s66, 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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66))))),
% 1.31/1.30 inference(monotonicity,[status(thm)],[5692])).
% 1.31/1.30 tff(5694,plain,
% 1.31/1.30 (((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)) | m_main_v_state1(s66, 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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)))),
% 1.31/1.30 inference(transitivity,[status(thm)],[5693, 5691])).
% 1.31/1.30 tff(5695,plain,
% 1.31/1.30 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66)) | m_main_v_state1(s66, c_c1))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5696,plain,
% 1.31/1.30 ((~![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(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65) | (~node7(s65, s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 1.31/1.30 tff(5697,plain,
% 1.31/1.30 ((~m_main_v_state1(s65, c_t1)) | (~m_main_v_state2(s65, c_n2)) | m_main_v_state1(s66, c_c1) | node1(s65) | node2(s65) | node3(s65)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5696, 892, 5690])).
% 1.31/1.30 tff(5698,plain,
% 1.31/1.30 (m_main_v_state1(s66, c_c1)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5697, 5686, 5599, 5563, 5682, 5671])).
% 1.31/1.30 tff(5699,plain,
% 1.31/1.30 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s66, c_n1)) | (~m_main_v_state1(s66, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s66, c_n1)) | (~m_main_v_state1(s66, c_c1)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5700,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s66, c_n1)) | (~m_main_v_state1(s66, c_c1)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5701,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s66, c_n1)) | (~m_main_v_state1(s66, c_c1))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5700, 5699])).
% 1.31/1.30 tff(5702,plain,
% 1.31/1.30 (~m_main_v_state1(s66, c_n1)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5701, 454, 5698])).
% 1.31/1.30 tff(5703,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s66, c_n1) | (~node11(s66)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s66, c_n1) | (~node11(s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5704,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s66, c_n1) | (~node11(s66)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5705,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s66, c_n1) | (~node11(s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5704, 5703])).
% 1.31/1.30 tff(5706,plain,
% 1.31/1.30 (~node11(s66)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5705, 238, 5702])).
% 1.31/1.30 tff(5707,plain,
% 1.31/1.30 (succ(s66, s67) <=> succ(s66, s67)),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5708,axiom,(succ(s66, s67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound67')).
% 1.31/1.30 tff(5709,plain,
% 1.31/1.30 (succ(s66, s67)),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5708, 5707])).
% 1.31/1.30 tff(5710,plain,
% 1.31/1.30 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5711,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5712,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67)),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5711, 5710])).
% 1.31/1.30 tff(5713,plain,
% 1.31/1.30 (trans(s66, s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5712, 5709, 39])).
% 1.31/1.30 tff(5714,plain,
% 1.31/1.30 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s66, s67)) | node14(s66, s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s66, s67)) | node14(s66, s67))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5715,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s66, s67)) | node14(s66, s67))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5716,plain,
% 1.31/1.30 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s66, s67)) | node14(s66, s67)),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5715, 5714])).
% 1.31/1.30 tff(5717,plain,
% 1.31/1.30 (node14(s66, s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5716, 7, 5713])).
% 1.31/1.30 tff(5718,plain,
% 1.31/1.30 (((~![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(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67) | (~node14(s66, s67)))) <=> ((~![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(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67) | (~node14(s66, s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5719,plain,
% 1.31/1.30 ((~![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(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67) | (~node14(s66, s67)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5720,plain,
% 1.31/1.30 ((~![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(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67) | (~node14(s66, s67))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5719, 5718])).
% 1.31/1.30 tff(5721,plain,
% 1.31/1.30 (m_main_v_state2(s66, c_c2) | node9(s66) | node8(s66) | node10(s66) | node11(s66) | node12(s66) | node13(s66, s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5720, 296, 5717])).
% 1.31/1.30 tff(5722,plain,
% 1.31/1.30 (node13(s66, s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5721, 5706, 5663, 5659, 5655, 5651, 5634])).
% 1.31/1.30 tff(5723,plain,
% 1.31/1.30 (((~![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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67)))) <=> ((~![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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5724,plain,
% 1.31/1.30 (((~node13(s66, s67)) | m_main_v_state2(s66, c_n2) | (~m_main_v_state2(s67, c_n2))) <=> (m_main_v_state2(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5725,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s66, s67)) | m_main_v_state2(s66, c_n2) | (~m_main_v_state2(s67, 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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67))))),
% 1.31/1.30 inference(monotonicity,[status(thm)],[5724])).
% 1.31/1.30 tff(5726,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s66, s67)) | m_main_v_state2(s66, c_n2) | (~m_main_v_state2(s67, 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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67)))),
% 1.31/1.30 inference(transitivity,[status(thm)],[5725, 5723])).
% 1.31/1.30 tff(5727,plain,
% 1.31/1.30 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s66, s67)) | m_main_v_state2(s66, c_n2) | (~m_main_v_state2(s67, c_n2)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5728,plain,
% 1.31/1.30 ((~![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(s66, c_n2) | (~m_main_v_state2(s67, c_n2)) | (~node13(s66, s67))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5727, 5726])).
% 1.31/1.30 tff(5729,plain,
% 1.31/1.30 (~m_main_v_state2(s67, c_n2)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5728, 311, 5647, 5722])).
% 1.31/1.30 tff(5730,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s67, c_n2) | (~node9(s67)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s67, c_n2) | (~node9(s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5731,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s67, c_n2) | (~node9(s67)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5732,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s67, c_n2) | (~node9(s67))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5731, 5730])).
% 1.31/1.30 tff(5733,plain,
% 1.31/1.30 (~node9(s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5732, 88, 5729])).
% 1.31/1.30 tff(5734,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s67, c_n2) | (~node10(s67)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s67, c_n2) | (~node10(s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5735,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s67, c_n2) | (~node10(s67)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5736,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s67, c_n2) | (~node10(s67))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5735, 5734])).
% 1.31/1.30 tff(5737,plain,
% 1.31/1.30 (~node10(s67)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5736, 249, 5729])).
% 1.31/1.30 tff(5738,plain,
% 1.31/1.30 (((~![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(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67)))) <=> ((~![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(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5739,plain,
% 1.31/1.30 (((~node13(s66, s67)) | (~m_main_v_state2(s66, c_t2)) | m_main_v_state2(s67, c_t2)) <=> ((~m_main_v_state2(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5740,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s66, s67)) | (~m_main_v_state2(s66, c_t2)) | m_main_v_state2(s67, 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(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67))))),
% 1.31/1.30 inference(monotonicity,[status(thm)],[5739])).
% 1.31/1.30 tff(5741,plain,
% 1.31/1.30 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s66, s67)) | (~m_main_v_state2(s66, c_t2)) | m_main_v_state2(s67, 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(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67)))),
% 1.31/1.30 inference(transitivity,[status(thm)],[5740, 5738])).
% 1.31/1.30 tff(5742,plain,
% 1.31/1.30 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s66, s67)) | (~m_main_v_state2(s66, c_t2)) | m_main_v_state2(s67, c_t2))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5743,plain,
% 1.31/1.30 ((~![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(s66, c_t2)) | m_main_v_state2(s67, c_t2) | (~node13(s66, s67))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5742, 5741])).
% 1.31/1.30 tff(5744,plain,
% 1.31/1.30 (m_main_v_state2(s67, c_t2)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5743, 518, 5643, 5722])).
% 1.31/1.30 tff(5745,plain,
% 1.31/1.30 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s66, c_t1)) | (~m_main_v_state1(s66, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s66, c_t1)) | (~m_main_v_state1(s66, c_c1)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5746,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s66, c_t1)) | (~m_main_v_state1(s66, c_c1)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5747,plain,
% 1.31/1.30 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s66, c_t1)) | (~m_main_v_state1(s66, c_c1))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5746, 5745])).
% 1.31/1.30 tff(5748,plain,
% 1.31/1.30 (~m_main_v_state1(s66, c_t1)),
% 1.31/1.30 inference(unit_resolution,[status(thm)],[5747, 539, 5698])).
% 1.31/1.30 tff(5749,plain,
% 1.31/1.30 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s66, c_t1) | (~node5(s66)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s66, c_t1) | (~node5(s66)))),
% 1.31/1.30 inference(rewrite,[status(thm)],[])).
% 1.31/1.30 tff(5750,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s66, c_t1) | (~node5(s66)))),
% 1.31/1.30 inference(quant_inst,[status(thm)],[])).
% 1.31/1.30 tff(5751,plain,
% 1.31/1.30 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s66, c_t1) | (~node5(s66))),
% 1.31/1.30 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 1.31/1.31 tff(5752,plain,
% 1.31/1.31 (~node5(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5751, 550, 5748])).
% 1.31/1.31 tff(5753,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s66, c_n2) | (~node4(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s66, c_n2) | (~node4(s66)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5754,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s66, c_n2) | (~node4(s66)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5755,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s66, c_n2) | (~node4(s66))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5754, 5753])).
% 1.31/1.31 tff(5756,plain,
% 1.31/1.31 (~node4(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5755, 388, 5647])).
% 1.31/1.31 tff(5757,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s66, c_c2) | (~node3(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s66, c_c2) | (~node3(s66)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5758,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s66, c_c2) | (~node3(s66)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5759,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s66, c_c2) | (~node3(s66))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 1.31/1.31 tff(5760,plain,
% 1.31/1.31 (~node3(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5759, 399, 5663])).
% 1.31/1.31 tff(5761,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s66, c_n2) | (~node2(s66)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s66, c_n2) | (~node2(s66)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5762,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s66, c_n2) | (~node2(s66)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5763,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s66, c_n2) | (~node2(s66))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5762, 5761])).
% 1.31/1.31 tff(5764,plain,
% 1.31/1.31 (~node2(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5763, 410, 5647])).
% 1.31/1.31 tff(5765,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s66, c_n1) | (~node1(s66)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s66, c_n1) | (~node1(s66)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5766,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s66, c_n1) | (~node1(s66)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5767,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s66, c_n1) | (~node1(s66))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5766, 5765])).
% 1.31/1.31 tff(5768,plain,
% 1.31/1.31 (~node1(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5767, 421, 5702])).
% 1.31/1.31 tff(5769,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s66, s67)) | node7(s66, s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s66, s67)) | node7(s66, s67))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5770,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s66, s67)) | node7(s66, s67))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5771,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s66, s67)) | node7(s66, s67)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5770, 5769])).
% 1.31/1.31 tff(5772,plain,
% 1.31/1.31 (node7(s66, s67)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5771, 206, 5713])).
% 1.31/1.31 tff(5773,plain,
% 1.31/1.31 (((~![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(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)))) <=> ((~![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(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5774,plain,
% 1.31/1.31 (((~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)) | m_main_v_state1(s67, c_n1)) <=> (m_main_v_state1(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5775,plain,
% 1.31/1.31 (((~![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(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)) | m_main_v_state1(s67, 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(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67))))),
% 1.31/1.31 inference(monotonicity,[status(thm)],[5774])).
% 1.31/1.31 tff(5776,plain,
% 1.31/1.31 (((~![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(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)) | m_main_v_state1(s67, 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(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)))),
% 1.31/1.31 inference(transitivity,[status(thm)],[5775, 5773])).
% 1.31/1.31 tff(5777,plain,
% 1.31/1.31 ((~![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(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67)) | m_main_v_state1(s67, c_n1))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5778,plain,
% 1.31/1.31 ((~![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(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66) | (~node7(s66, s67))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5777, 5776])).
% 1.31/1.31 tff(5779,plain,
% 1.31/1.31 (m_main_v_state1(s67, c_n1) | (~m_main_v_state1(s66, c_c1)) | node1(s66) | node2(s66) | node3(s66) | node4(s66) | node5(s66)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5778, 584, 5772])).
% 1.31/1.31 tff(5780,plain,
% 1.31/1.31 (m_main_v_state1(s67, c_n1)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5779, 5768, 5698, 5764, 5760, 5756, 5752])).
% 1.31/1.31 tff(5781,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s67, c_n2) | (~node8(s67)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s67, c_n2) | (~node8(s67)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5782,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s67, c_n2) | (~node8(s67)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5783,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s67, c_n2) | (~node8(s67))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5782, 5781])).
% 1.31/1.31 tff(5784,plain,
% 1.31/1.31 (~node8(s67)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5783, 271, 5729])).
% 1.31/1.31 tff(5785,plain,
% 1.31/1.31 (succ(s67, s68) <=> succ(s67, s68)),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5786,axiom,(succ(s67, s68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound68')).
% 1.31/1.31 tff(5787,plain,
% 1.31/1.31 (succ(s67, s68)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5786, 5785])).
% 1.31/1.31 tff(5788,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5789,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5790,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 1.31/1.31 tff(5791,plain,
% 1.31/1.31 (trans(s67, s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5790, 5787, 39])).
% 1.31/1.31 tff(5792,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s67, s68)) | node14(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s67, s68)) | node14(s67, s68))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5793,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s67, s68)) | node14(s67, s68))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5794,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s67, s68)) | node14(s67, s68)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5793, 5792])).
% 1.31/1.31 tff(5795,plain,
% 1.31/1.31 (node14(s67, s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5794, 7, 5791])).
% 1.31/1.31 tff(5796,plain,
% 1.31/1.31 (((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | node9(s67) | node8(s67) | node10(s67) | (~node14(s67, s68)) | m_main_v_state2(s68, 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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | node9(s67) | node8(s67) | node10(s67) | (~node14(s67, s68)) | m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5797,plain,
% 1.31/1.31 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | node9(s67) | node8(s67) | node10(s67) | (~node14(s67, s68)) | m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5798,plain,
% 1.31/1.31 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | node9(s67) | node8(s67) | node10(s67) | (~node14(s67, s68)) | m_main_v_state2(s68, c_c2)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5797, 5796])).
% 1.31/1.31 tff(5799,plain,
% 1.31/1.31 ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | node9(s67) | node8(s67) | node10(s67) | m_main_v_state2(s68, c_c2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5798, 617, 5795])).
% 1.31/1.31 tff(5800,plain,
% 1.31/1.31 (m_main_v_state2(s68, c_c2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5799, 5784, 5780, 5744, 5737, 5733])).
% 1.31/1.31 tff(5801,plain,
% 1.31/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s68, c_t2)) | (~m_main_v_state2(s68, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s68, c_t2)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5802,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s68, c_t2)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5803,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s68, c_t2)) | (~m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 1.31/1.31 tff(5804,plain,
% 1.31/1.31 (~m_main_v_state2(s68, c_t2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5803, 260, 5800])).
% 1.31/1.31 tff(5805,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s68, c_t2) | (~node12(s68)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s68, c_t2) | (~node12(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5806,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s68, c_t2) | (~node12(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5807,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s68, c_t2) | (~node12(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5806, 5805])).
% 1.31/1.31 tff(5808,plain,
% 1.31/1.31 (~node12(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5807, 633, 5804])).
% 1.31/1.31 tff(5809,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s67, s68)) | node7(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s67, s68)) | node7(s67, s68))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5810,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s67, s68)) | node7(s67, s68))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5811,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s67, s68)) | node7(s67, s68)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 1.31/1.31 tff(5812,plain,
% 1.31/1.31 (node7(s67, s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5811, 206, 5791])).
% 1.31/1.31 tff(5813,plain,
% 1.31/1.31 (((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node7(s67, s68)) | m_main_v_state1(s68, 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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node7(s67, s68)) | m_main_v_state1(s68, c_t1))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5814,plain,
% 1.31/1.31 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node7(s67, s68)) | m_main_v_state1(s68, c_t1))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5815,plain,
% 1.31/1.31 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node7(s67, s68)) | m_main_v_state1(s68, c_t1)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5814, 5813])).
% 1.31/1.31 tff(5816,plain,
% 1.31/1.31 ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | m_main_v_state1(s68, c_t1)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5815, 651, 5812])).
% 1.31/1.31 tff(5817,plain,
% 1.31/1.31 (m_main_v_state1(s68, c_t1)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5816, 5744, 5780])).
% 1.31/1.31 tff(5818,plain,
% 1.31/1.31 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s68, c_n1)) | (~m_main_v_state1(s68, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s68, c_n1)) | (~m_main_v_state1(s68, c_t1)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5819,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s68, c_n1)) | (~m_main_v_state1(s68, c_t1)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5820,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s68, c_n1)) | (~m_main_v_state1(s68, c_t1))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5819, 5818])).
% 1.31/1.31 tff(5821,plain,
% 1.31/1.31 (~m_main_v_state1(s68, c_n1)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5820, 17, 5817])).
% 1.31/1.31 tff(5822,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s68, c_n1) | (~node11(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s68, c_n1) | (~node11(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5823,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s68, c_n1) | (~node11(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5824,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s68, c_n1) | (~node11(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 1.31/1.31 tff(5825,plain,
% 1.31/1.31 (~node11(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5824, 238, 5821])).
% 1.31/1.31 tff(5826,plain,
% 1.31/1.31 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s68, c_t1)) | (~m_main_v_state1(s68, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s68, c_t1)) | (~m_main_v_state1(s68, c_c1)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5827,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s68, c_t1)) | (~m_main_v_state1(s68, c_c1)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5828,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s68, c_t1)) | (~m_main_v_state1(s68, c_c1))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5827, 5826])).
% 1.31/1.31 tff(5829,plain,
% 1.31/1.31 (~m_main_v_state1(s68, c_c1)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5828, 539, 5817])).
% 1.31/1.31 tff(5830,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s68, c_c1) | (~node10(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s68, c_c1) | (~node10(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5831,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s68, c_c1) | (~node10(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5832,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s68, c_c1) | (~node10(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5831, 5830])).
% 1.31/1.31 tff(5833,plain,
% 1.31/1.31 (~node10(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5832, 675, 5829])).
% 1.31/1.31 tff(5834,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s68, c_n1) | (~node9(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s68, c_n1) | (~node9(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5835,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s68, c_n1) | (~node9(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5836,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s68, c_n1) | (~node9(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5835, 5834])).
% 1.31/1.31 tff(5837,plain,
% 1.31/1.31 (~node9(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5836, 686, 5821])).
% 1.31/1.31 tff(5838,plain,
% 1.31/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s68, c_n2)) | (~m_main_v_state2(s68, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s68, c_n2)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5839,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s68, c_n2)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5840,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s68, c_n2)) | (~m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5839, 5838])).
% 1.31/1.31 tff(5841,plain,
% 1.31/1.31 (~m_main_v_state2(s68, c_n2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5840, 697, 5800])).
% 1.31/1.31 tff(5842,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s68, c_n2) | (~node8(s68)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s68, c_n2) | (~node8(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5843,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s68, c_n2) | (~node8(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5844,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s68, c_n2) | (~node8(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5843, 5842])).
% 1.31/1.31 tff(5845,plain,
% 1.31/1.31 (~node8(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5844, 271, 5841])).
% 1.31/1.31 tff(5846,plain,
% 1.31/1.31 (succ(s68, s69) <=> succ(s68, s69)),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5847,axiom,(succ(s68, s69)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound69')).
% 1.31/1.31 tff(5848,plain,
% 1.31/1.31 (succ(s68, s69)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5847, 5846])).
% 1.31/1.31 tff(5849,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5850,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5851,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5850, 5849])).
% 1.31/1.31 tff(5852,plain,
% 1.31/1.31 (trans(s68, s69)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5851, 5848, 39])).
% 1.31/1.31 tff(5853,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s68, s69)) | node14(s68, s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s68, s69)) | node14(s68, s69))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5854,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s68, s69)) | node14(s68, s69))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5855,plain,
% 1.31/1.31 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s68, s69)) | node14(s68, s69)),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 1.31/1.31 tff(5856,plain,
% 1.31/1.31 (node14(s68, s69)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5855, 7, 5852])).
% 1.31/1.31 tff(5857,plain,
% 1.31/1.31 (((~![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(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, 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(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5858,plain,
% 1.31/1.31 (((~m_main_v_state2(s68, c_c2)) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | m_main_v_state2(s69, c_n2)) <=> (m_main_v_state2(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5859,plain,
% 1.31/1.31 (((~![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(s68, c_c2)) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | m_main_v_state2(s69, 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(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, c_c2))))),
% 1.31/1.31 inference(monotonicity,[status(thm)],[5858])).
% 1.31/1.31 tff(5860,plain,
% 1.31/1.31 (((~![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(s68, c_c2)) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | m_main_v_state2(s69, 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(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, c_c2)))),
% 1.31/1.31 inference(transitivity,[status(thm)],[5859, 5857])).
% 1.31/1.31 tff(5861,plain,
% 1.31/1.31 ((~![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(s68, c_c2)) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | m_main_v_state2(s69, c_n2))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5862,plain,
% 1.31/1.31 ((~![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(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~node14(s68, s69)) | (~m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5861, 5860])).
% 1.31/1.31 tff(5863,plain,
% 1.31/1.31 (m_main_v_state2(s69, c_n2) | node9(s68) | node8(s68) | node10(s68) | node11(s68) | node12(s68) | (~m_main_v_state2(s68, c_c2))),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5862, 726, 5856])).
% 1.31/1.31 tff(5864,plain,
% 1.31/1.31 (m_main_v_state2(s69, c_n2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5863, 5845, 5800, 5837, 5833, 5825, 5808])).
% 1.31/1.31 tff(5865,plain,
% 1.31/1.31 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_c2)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5866,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_c2)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5867,plain,
% 1.31/1.31 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_c2))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 1.31/1.31 tff(5868,plain,
% 1.31/1.31 (~m_main_v_state2(s69, c_c2)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5867, 697, 5864])).
% 1.31/1.31 tff(5869,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s69, c_c2) | (~node3(s69)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s69, c_c2) | (~node3(s69)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5870,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s69, c_c2) | (~node3(s69)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5871,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s69, c_c2) | (~node3(s69))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 1.31/1.31 tff(5872,plain,
% 1.31/1.31 (~node3(s69)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5871, 399, 5868])).
% 1.31/1.31 tff(5873,plain,
% 1.31/1.31 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s68, c_n1) | (~node1(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s68, c_n1) | (~node1(s68)))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.31 tff(5874,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s68, c_n1) | (~node1(s68)))),
% 1.31/1.31 inference(quant_inst,[status(thm)],[])).
% 1.31/1.31 tff(5875,plain,
% 1.31/1.31 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s68, c_n1) | (~node1(s68))),
% 1.31/1.31 inference(modus_ponens,[status(thm)],[5874, 5873])).
% 1.31/1.31 tff(5876,plain,
% 1.31/1.31 (~node1(s68)),
% 1.31/1.31 inference(unit_resolution,[status(thm)],[5875, 421, 5821])).
% 1.31/1.31 tff(5877,plain,
% 1.31/1.31 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s67, s68)) | node18(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s67, s68)) | node18(s67, s68))),
% 1.31/1.31 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5878,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s67, s68)) | node18(s67, s68))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5879,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s67, s68)) | node18(s67, s68)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5878, 5877])).
% 1.31/1.32 tff(5880,plain,
% 1.31/1.32 (node18(s67, s68)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5879, 125, 5791])).
% 1.31/1.32 tff(5881,plain,
% 1.31/1.32 (((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node18(s67, s68)) | m_main_v_turn(s68, 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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node18(s67, s68)) | m_main_v_turn(s68, c_2))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5882,plain,
% 1.31/1.32 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node18(s67, s68)) | m_main_v_turn(s68, c_2))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5883,plain,
% 1.31/1.32 ((~![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(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | (~node18(s67, s68)) | m_main_v_turn(s68, c_2)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5882, 5881])).
% 1.31/1.32 tff(5884,plain,
% 1.31/1.32 ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state2(s67, c_t2)) | m_main_v_turn(s68, c_2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5883, 760, 5880])).
% 1.31/1.32 tff(5885,plain,
% 1.31/1.32 (m_main_v_turn(s68, c_2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5884, 5744, 5780])).
% 1.31/1.32 tff(5886,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s68, c_1)) | (~m_main_v_turn(s68, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s68, c_1)) | (~m_main_v_turn(s68, c_2)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5887,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s68, c_1)) | (~m_main_v_turn(s68, c_2)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5888,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s68, c_1)) | (~m_main_v_turn(s68, c_2))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5887, 5886])).
% 1.31/1.32 tff(5889,plain,
% 1.31/1.32 (~m_main_v_turn(s68, c_1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5888, 156, 5885])).
% 1.31/1.32 tff(5890,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s68, c_1) | (~node5(s68)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s68, c_1) | (~node5(s68)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5891,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s68, c_1) | (~node5(s68)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5892,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s68, c_1) | (~node5(s68))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5891, 5890])).
% 1.31/1.32 tff(5893,plain,
% 1.31/1.32 (~node5(s68)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5892, 776, 5889])).
% 1.31/1.32 tff(5894,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s68, c_n1) | (~node2(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s68, c_n1) | (~node2(s68)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5895,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s68, c_n1) | (~node2(s68)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5896,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s68, c_n1) | (~node2(s68))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 1.31/1.32 tff(5897,plain,
% 1.31/1.32 (~node2(s68)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5896, 787, 5821])).
% 1.31/1.32 tff(5898,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s68, c_n1) | (~node3(s68)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s68, c_n1) | (~node3(s68)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5899,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s68, c_n1) | (~node3(s68)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5900,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s68, c_n1) | (~node3(s68))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5899, 5898])).
% 1.31/1.32 tff(5901,plain,
% 1.31/1.32 (~node3(s68)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5900, 798, 5821])).
% 1.31/1.32 tff(5902,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s68, c_n2) | (~node4(s68)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s68, c_n2) | (~node4(s68)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5903,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s68, c_n2) | (~node4(s68)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5904,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s68, c_n2) | (~node4(s68))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 1.31/1.32 tff(5905,plain,
% 1.31/1.32 (~node4(s68)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5904, 388, 5841])).
% 1.31/1.32 tff(5906,plain,
% 1.31/1.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s68, s69)) | node7(s68, s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s68, s69)) | node7(s68, s69))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5907,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s68, s69)) | node7(s68, s69))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5908,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s68, s69)) | node7(s68, s69)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5907, 5906])).
% 1.31/1.32 tff(5909,plain,
% 1.31/1.32 (node7(s68, s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5908, 206, 5852])).
% 1.31/1.32 tff(5910,plain,
% 1.31/1.32 (((~![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(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69)))) <=> ((~![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(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5911,plain,
% 1.31/1.32 ((~![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(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5912,plain,
% 1.31/1.32 ((~![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(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69) | (~node7(s68, s69))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.31/1.32 tff(5913,plain,
% 1.31/1.32 (m_main_v_state1(s68, c_c1) | node1(s68) | node2(s68) | node3(s68) | node4(s68) | node5(s68) | node6(s68, s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5912, 820, 5909])).
% 1.31/1.32 tff(5914,plain,
% 1.31/1.32 (node6(s68, s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5913, 5905, 5829, 5901, 5897, 5893, 5876])).
% 1.31/1.32 tff(5915,plain,
% 1.31/1.32 (((~![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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69)))) <=> ((~![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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5916,plain,
% 1.31/1.32 (((~node6(s68, s69)) | m_main_v_state1(s68, c_n1) | (~m_main_v_state1(s69, c_n1))) <=> (m_main_v_state1(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5917,plain,
% 1.31/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s68, s69)) | m_main_v_state1(s68, c_n1) | (~m_main_v_state1(s69, 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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69))))),
% 1.31/1.32 inference(monotonicity,[status(thm)],[5916])).
% 1.31/1.32 tff(5918,plain,
% 1.31/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s68, s69)) | m_main_v_state1(s68, c_n1) | (~m_main_v_state1(s69, 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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69)))),
% 1.31/1.32 inference(transitivity,[status(thm)],[5917, 5915])).
% 1.31/1.32 tff(5919,plain,
% 1.31/1.32 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s68, s69)) | m_main_v_state1(s68, c_n1) | (~m_main_v_state1(s69, c_n1)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5920,plain,
% 1.31/1.32 ((~![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(s68, c_n1) | (~m_main_v_state1(s69, c_n1)) | (~node6(s68, s69))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 1.31/1.32 tff(5921,plain,
% 1.31/1.32 (~m_main_v_state1(s69, c_n1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5920, 835, 5821, 5914])).
% 1.31/1.32 tff(5922,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s69, c_n1) | (~node2(s69)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s69, c_n1) | (~node2(s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5923,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s69, c_n1) | (~node2(s69)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5924,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s69, c_n1) | (~node2(s69))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5923, 5922])).
% 1.31/1.32 tff(5925,plain,
% 1.31/1.32 (~node2(s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5924, 787, 5921])).
% 1.31/1.32 tff(5926,plain,
% 1.31/1.32 (((~![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(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69)))) <=> ((~![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(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5927,plain,
% 1.31/1.32 (((~node6(s68, s69)) | (~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, c_t1)) <=> ((~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5928,plain,
% 1.31/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s68, s69)) | (~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, 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(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69))))),
% 1.31/1.32 inference(monotonicity,[status(thm)],[5927])).
% 1.31/1.32 tff(5929,plain,
% 1.31/1.32 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s68, s69)) | (~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, 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(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69)))),
% 1.31/1.32 inference(transitivity,[status(thm)],[5928, 5926])).
% 1.31/1.32 tff(5930,plain,
% 1.31/1.32 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s68, s69)) | (~m_main_v_state1(s68, c_t1)) | m_main_v_state1(s69, c_t1))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5931,plain,
% 1.31/1.32 ((~![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(s68, c_t1)) | m_main_v_state1(s69, c_t1) | (~node6(s68, s69))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5930, 5929])).
% 1.31/1.32 tff(5932,plain,
% 1.31/1.32 (m_main_v_state1(s69, c_t1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5931, 856, 5817, 5914])).
% 1.31/1.32 tff(5933,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_t2)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5934,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_t2)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5935,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s69, c_n2)) | (~m_main_v_state2(s69, c_t2))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5934, 5933])).
% 1.31/1.32 tff(5936,plain,
% 1.31/1.32 (~m_main_v_state2(s69, c_t2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5935, 77, 5864])).
% 1.31/1.32 tff(5937,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s69, c_t2) | (~node1(s69)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s69, c_t2) | (~node1(s69)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5938,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s69, c_t2) | (~node1(s69)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5939,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s69, c_t2) | (~node1(s69))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5938, 5937])).
% 1.31/1.32 tff(5940,plain,
% 1.31/1.32 (~node1(s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5939, 195, 5936])).
% 1.31/1.32 tff(5941,plain,
% 1.31/1.32 (succ(s69, s70) <=> succ(s69, s70)),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5942,axiom,(succ(s69, s70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound70')).
% 1.31/1.32 tff(5943,plain,
% 1.31/1.32 (succ(s69, s70)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5942, 5941])).
% 1.31/1.32 tff(5944,plain,
% 1.31/1.32 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5945,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5946,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5945, 5944])).
% 1.31/1.32 tff(5947,plain,
% 1.31/1.32 (trans(s69, s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5946, 5943, 39])).
% 1.31/1.32 tff(5948,plain,
% 1.31/1.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s69, s70)) | node7(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s69, s70)) | node7(s69, s70))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5949,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s69, s70)) | node7(s69, s70))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5950,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s69, s70)) | node7(s69, s70)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5949, 5948])).
% 1.31/1.32 tff(5951,plain,
% 1.31/1.32 (node7(s69, s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5950, 206, 5947])).
% 1.31/1.32 tff(5952,plain,
% 1.31/1.32 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)))) <=> ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5953,plain,
% 1.31/1.32 (((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)) | m_main_v_state1(s70, c_c1)) <=> ((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5954,plain,
% 1.31/1.32 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)) | m_main_v_state1(s70, 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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70))))),
% 1.31/1.32 inference(monotonicity,[status(thm)],[5953])).
% 1.31/1.32 tff(5955,plain,
% 1.31/1.32 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)) | m_main_v_state1(s70, 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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)))),
% 1.31/1.32 inference(transitivity,[status(thm)],[5954, 5952])).
% 1.31/1.32 tff(5956,plain,
% 1.31/1.32 ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70)) | m_main_v_state1(s70, c_c1))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5957,plain,
% 1.31/1.32 ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69) | (~node7(s69, s70))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 1.31/1.32 tff(5958,plain,
% 1.31/1.32 ((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state1(s70, c_c1) | node1(s69) | node2(s69) | node3(s69)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5957, 892, 5951])).
% 1.31/1.32 tff(5959,plain,
% 1.31/1.32 (m_main_v_state1(s70, c_c1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5958, 5940, 5864, 5932, 5925, 5872])).
% 1.31/1.32 tff(5960,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s70, c_t1)) | (~m_main_v_state1(s70, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s70, c_t1)) | (~m_main_v_state1(s70, c_c1)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5961,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s70, c_t1)) | (~m_main_v_state1(s70, c_c1)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5962,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s70, c_t1)) | (~m_main_v_state1(s70, c_c1))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5961, 5960])).
% 1.31/1.32 tff(5963,plain,
% 1.31/1.32 (~m_main_v_state1(s70, c_t1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5962, 539, 5959])).
% 1.31/1.32 tff(5964,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s70, c_t1) | (~node5(s70)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s70, c_t1) | (~node5(s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5965,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s70, c_t1) | (~node5(s70)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5966,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s70, c_t1) | (~node5(s70))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 1.31/1.32 tff(5967,plain,
% 1.31/1.32 (~node5(s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5966, 550, 5963])).
% 1.31/1.32 tff(5968,plain,
% 1.31/1.32 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s69, s70)) | node14(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s69, s70)) | node14(s69, s70))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5969,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s69, s70)) | node14(s69, s70))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5970,plain,
% 1.31/1.32 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s69, s70)) | node14(s69, s70)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 1.31/1.32 tff(5971,plain,
% 1.31/1.32 (node14(s69, s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5970, 7, 5947])).
% 1.31/1.32 tff(5972,plain,
% 1.31/1.32 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, 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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, c_t2))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5973,plain,
% 1.31/1.32 ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, c_t2))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5974,plain,
% 1.31/1.32 ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | (~node14(s69, s70)) | m_main_v_state2(s70, c_t2)),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5973, 5972])).
% 1.31/1.32 tff(5975,plain,
% 1.31/1.32 ((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_state2(s70, c_t2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5974, 922, 5971])).
% 1.31/1.32 tff(5976,plain,
% 1.31/1.32 (m_main_v_state2(s70, c_t2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5975, 5932, 5864])).
% 1.31/1.32 tff(5977,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s70, c_n2)) | (~m_main_v_state2(s70, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s70, c_n2)) | (~m_main_v_state2(s70, c_t2)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5978,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s70, c_n2)) | (~m_main_v_state2(s70, c_t2)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5979,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s70, c_n2)) | (~m_main_v_state2(s70, c_t2))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 1.31/1.32 tff(5980,plain,
% 1.31/1.32 (~m_main_v_state2(s70, c_n2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5979, 77, 5976])).
% 1.31/1.32 tff(5981,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s70, c_n2) | (~node4(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s70, c_n2) | (~node4(s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5982,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s70, c_n2) | (~node4(s70)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5983,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s70, c_n2) | (~node4(s70))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5982, 5981])).
% 1.31/1.32 tff(5984,plain,
% 1.31/1.32 (~node4(s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5983, 388, 5980])).
% 1.31/1.32 tff(5985,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s70, c_t2)) | (~m_main_v_state2(s70, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s70, c_t2)) | (~m_main_v_state2(s70, c_c2)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5986,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s70, c_t2)) | (~m_main_v_state2(s70, c_c2)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5987,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s70, c_t2)) | (~m_main_v_state2(s70, c_c2))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5986, 5985])).
% 1.31/1.32 tff(5988,plain,
% 1.31/1.32 (~m_main_v_state2(s70, c_c2)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5987, 260, 5976])).
% 1.31/1.32 tff(5989,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s70, c_c2) | (~node3(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s70, c_c2) | (~node3(s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5990,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s70, c_c2) | (~node3(s70)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5991,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s70, c_c2) | (~node3(s70))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 1.31/1.32 tff(5992,plain,
% 1.31/1.32 (~node3(s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5991, 399, 5988])).
% 1.31/1.32 tff(5993,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s70, c_n2) | (~node2(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s70, c_n2) | (~node2(s70)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5994,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s70, c_n2) | (~node2(s70)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5995,plain,
% 1.31/1.32 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s70, c_n2) | (~node2(s70))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 1.31/1.32 tff(5996,plain,
% 1.31/1.32 (~node2(s70)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5995, 410, 5980])).
% 1.31/1.32 tff(5997,plain,
% 1.31/1.32 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s70, c_n1)) | (~m_main_v_state1(s70, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s70, c_n1)) | (~m_main_v_state1(s70, c_c1)))),
% 1.31/1.32 inference(rewrite,[status(thm)],[])).
% 1.31/1.32 tff(5998,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s70, c_n1)) | (~m_main_v_state1(s70, c_c1)))),
% 1.31/1.32 inference(quant_inst,[status(thm)],[])).
% 1.31/1.32 tff(5999,plain,
% 1.31/1.32 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s70, c_n1)) | (~m_main_v_state1(s70, c_c1))),
% 1.31/1.32 inference(modus_ponens,[status(thm)],[5998, 5997])).
% 1.31/1.32 tff(6000,plain,
% 1.31/1.32 (~m_main_v_state1(s70, c_n1)),
% 1.31/1.32 inference(unit_resolution,[status(thm)],[5999, 454, 5959])).
% 1.31/1.32 tff(6001,plain,
% 1.31/1.32 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s70, c_n1) | (~node1(s70)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s70, c_n1) | (~node1(s70)))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6002,plain,
% 1.31/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s70, c_n1) | (~node1(s70)))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6003,plain,
% 1.31/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s70, c_n1) | (~node1(s70))),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 1.31/1.33 tff(6004,plain,
% 1.31/1.33 (~node1(s70)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6003, 421, 6000])).
% 1.31/1.33 tff(6005,plain,
% 1.31/1.33 (succ(s70, s71) <=> succ(s70, s71)),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6006,axiom,(succ(s70, s71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound71')).
% 1.31/1.33 tff(6007,plain,
% 1.31/1.33 (succ(s70, s71)),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 1.31/1.33 tff(6008,plain,
% 1.31/1.33 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6009,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6010,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71)),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 1.31/1.33 tff(6011,plain,
% 1.31/1.33 (trans(s70, s71)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6010, 6007, 39])).
% 1.31/1.33 tff(6012,plain,
% 1.31/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s70, s71)) | node7(s70, s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s70, s71)) | node7(s70, s71))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6013,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s70, s71)) | node7(s70, s71))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6014,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s70, s71)) | node7(s70, s71)),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6013, 6012])).
% 1.31/1.33 tff(6015,plain,
% 1.31/1.33 (node7(s70, s71)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6014, 206, 6011])).
% 1.31/1.33 tff(6016,plain,
% 1.31/1.33 (((~![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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)))) <=> ((~![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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6017,plain,
% 1.31/1.33 (((~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)) | m_main_v_state1(s71, c_n1)) <=> (m_main_v_state1(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6018,plain,
% 1.31/1.33 (((~![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(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)) | m_main_v_state1(s71, 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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71))))),
% 1.31/1.33 inference(monotonicity,[status(thm)],[6017])).
% 1.31/1.33 tff(6019,plain,
% 1.31/1.33 (((~![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(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)) | m_main_v_state1(s71, 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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)))),
% 1.31/1.33 inference(transitivity,[status(thm)],[6018, 6016])).
% 1.31/1.33 tff(6020,plain,
% 1.31/1.33 ((~![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(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71)) | m_main_v_state1(s71, c_n1))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6021,plain,
% 1.31/1.33 ((~![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(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70) | (~node7(s70, s71))),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6020, 6019])).
% 1.31/1.33 tff(6022,plain,
% 1.31/1.33 (m_main_v_state1(s71, c_n1) | (~m_main_v_state1(s70, c_c1)) | node1(s70) | node2(s70) | node3(s70) | node4(s70) | node5(s70)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6021, 584, 6015])).
% 1.31/1.33 tff(6023,plain,
% 1.31/1.33 (m_main_v_state1(s71, c_n1)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6022, 6004, 5959, 5996, 5992, 5984, 5967])).
% 1.31/1.33 tff(6024,plain,
% 1.31/1.33 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s69, c_t2) | (~node15(s69)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s69, c_t2) | (~node15(s69)))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6025,plain,
% 1.31/1.33 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s69, c_t2) | (~node15(s69)))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6026,plain,
% 1.31/1.33 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s69, c_t2) | (~node15(s69))),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6025, 6024])).
% 1.31/1.33 tff(6027,plain,
% 1.31/1.33 (~node15(s69)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6026, 103, 5936])).
% 1.31/1.33 tff(6028,plain,
% 1.31/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s69, s70)) | node18(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s69, s70)) | node18(s69, s70))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6029,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s69, s70)) | node18(s69, s70))),
% 1.31/1.33 inference(quant_inst,[status(thm)],[])).
% 1.31/1.33 tff(6030,plain,
% 1.31/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s69, s70)) | node18(s69, s70)),
% 1.31/1.33 inference(modus_ponens,[status(thm)],[6029, 6028])).
% 1.31/1.33 tff(6031,plain,
% 1.31/1.33 (node18(s69, s70)),
% 1.31/1.33 inference(unit_resolution,[status(thm)],[6030, 125, 5947])).
% 1.31/1.33 tff(6032,plain,
% 1.31/1.33 (((~![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(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, 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(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6033,plain,
% 1.31/1.33 (((~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node15(s69) | (~node18(s69, s70)) | m_main_v_turn(s70, c_1)) <=> (node15(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1))),
% 1.31/1.33 inference(rewrite,[status(thm)],[])).
% 1.31/1.33 tff(6034,plain,
% 1.41/1.33 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node15(s69) | (~node18(s69, s70)) | m_main_v_turn(s70, 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(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1)))),
% 1.41/1.33 inference(monotonicity,[status(thm)],[6033])).
% 1.41/1.33 tff(6035,plain,
% 1.41/1.33 (((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node15(s69) | (~node18(s69, s70)) | m_main_v_turn(s70, 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(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1))),
% 1.41/1.33 inference(transitivity,[status(thm)],[6034, 6032])).
% 1.41/1.33 tff(6036,plain,
% 1.41/1.33 ((~![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(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | node15(s69) | (~node18(s69, s70)) | m_main_v_turn(s70, c_1))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6037,plain,
% 1.41/1.33 ((~![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(s69) | (~node18(s69, s70)) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6036, 6035])).
% 1.41/1.33 tff(6038,plain,
% 1.41/1.33 (node15(s69) | (~m_main_v_state1(s69, c_t1)) | (~m_main_v_state2(s69, c_n2)) | m_main_v_turn(s70, c_1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6037, 992, 6031])).
% 1.41/1.33 tff(6039,plain,
% 1.41/1.33 (m_main_v_turn(s70, c_1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6038, 6027, 5864, 5932])).
% 1.41/1.33 tff(6040,plain,
% 1.41/1.33 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s70, c_1)) | (~m_main_v_turn(s70, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s70, c_1)) | (~m_main_v_turn(s70, c_2)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6041,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s70, c_1)) | (~m_main_v_turn(s70, c_2)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6042,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s70, c_1)) | (~m_main_v_turn(s70, c_2))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6041, 6040])).
% 1.41/1.33 tff(6043,plain,
% 1.41/1.33 (~m_main_v_turn(s70, c_2)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6042, 156, 6039])).
% 1.41/1.33 tff(6044,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s70, c_2) | (~node12(s70)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s70, c_2) | (~node12(s70)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6045,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s70, c_2) | (~node12(s70)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6046,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s70, c_2) | (~node12(s70))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6045, 6044])).
% 1.41/1.33 tff(6047,plain,
% 1.41/1.33 (~node12(s70)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6046, 184, 6043])).
% 1.41/1.33 tff(6048,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s70, c_n2) | (~node8(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s70, c_n2) | (~node8(s70)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6049,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s70, c_n2) | (~node8(s70)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6050,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s70, c_n2) | (~node8(s70))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 1.41/1.33 tff(6051,plain,
% 1.41/1.33 (~node8(s70)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6050, 271, 5980])).
% 1.41/1.33 tff(6052,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s70, c_n2) | (~node9(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s70, c_n2) | (~node9(s70)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6053,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s70, c_n2) | (~node9(s70)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6054,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s70, c_n2) | (~node9(s70))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6053, 6052])).
% 1.41/1.33 tff(6055,plain,
% 1.41/1.33 (~node9(s70)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6054, 88, 5980])).
% 1.41/1.33 tff(6056,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s70, c_n2) | (~node10(s70)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s70, c_n2) | (~node10(s70)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6057,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s70, c_n2) | (~node10(s70)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6058,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s70, c_n2) | (~node10(s70))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 1.41/1.33 tff(6059,plain,
% 1.41/1.33 (~node10(s70)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6058, 249, 5980])).
% 1.41/1.33 tff(6060,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s70, c_n1) | (~node11(s70)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s70, c_n1) | (~node11(s70)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6061,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s70, c_n1) | (~node11(s70)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6062,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s70, c_n1) | (~node11(s70))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6061, 6060])).
% 1.41/1.33 tff(6063,plain,
% 1.41/1.33 (~node11(s70)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6062, 238, 6000])).
% 1.41/1.33 tff(6064,plain,
% 1.41/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s70, s71)) | node14(s70, s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s70, s71)) | node14(s70, s71))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6065,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s70, s71)) | node14(s70, s71))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6066,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s70, s71)) | node14(s70, s71)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6065, 6064])).
% 1.41/1.33 tff(6067,plain,
% 1.41/1.33 (node14(s70, s71)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6066, 7, 6011])).
% 1.41/1.33 tff(6068,plain,
% 1.41/1.33 (((~![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(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71)))) <=> ((~![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(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6069,plain,
% 1.41/1.33 ((~![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(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6070,plain,
% 1.41/1.33 ((~![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(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71) | (~node14(s70, s71))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6069, 6068])).
% 1.41/1.33 tff(6071,plain,
% 1.41/1.33 (m_main_v_state2(s70, c_c2) | node9(s70) | node8(s70) | node10(s70) | node11(s70) | node12(s70) | node13(s70, s71)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6070, 296, 6067])).
% 1.41/1.33 tff(6072,plain,
% 1.41/1.33 (node13(s70, s71)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6071, 6063, 5988, 6059, 6055, 6051, 6047])).
% 1.41/1.33 tff(6073,plain,
% 1.41/1.33 (((~![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(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71)))) <=> ((~![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(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6074,plain,
% 1.41/1.33 (((~node13(s70, s71)) | (~m_main_v_state2(s70, c_t2)) | m_main_v_state2(s71, c_t2)) <=> ((~m_main_v_state2(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6075,plain,
% 1.41/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s70, s71)) | (~m_main_v_state2(s70, c_t2)) | m_main_v_state2(s71, 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(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71))))),
% 1.41/1.33 inference(monotonicity,[status(thm)],[6074])).
% 1.41/1.33 tff(6076,plain,
% 1.41/1.33 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s70, s71)) | (~m_main_v_state2(s70, c_t2)) | m_main_v_state2(s71, 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(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71)))),
% 1.41/1.33 inference(transitivity,[status(thm)],[6075, 6073])).
% 1.41/1.33 tff(6077,plain,
% 1.41/1.33 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s70, s71)) | (~m_main_v_state2(s70, c_t2)) | m_main_v_state2(s71, c_t2))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6078,plain,
% 1.41/1.33 ((~![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(s70, c_t2)) | m_main_v_state2(s71, c_t2) | (~node13(s70, s71))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6077, 6076])).
% 1.41/1.33 tff(6079,plain,
% 1.41/1.33 (m_main_v_state2(s71, c_t2)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6078, 518, 5976, 6072])).
% 1.41/1.33 tff(6080,plain,
% 1.41/1.33 (succ(s71, s72) <=> succ(s71, s72)),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6081,axiom,(succ(s71, s72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound72')).
% 1.41/1.33 tff(6082,plain,
% 1.41/1.33 (succ(s71, s72)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6081, 6080])).
% 1.41/1.33 tff(6083,plain,
% 1.41/1.33 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6084,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6085,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6084, 6083])).
% 1.41/1.33 tff(6086,plain,
% 1.41/1.33 (trans(s71, s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6085, 6082, 39])).
% 1.41/1.33 tff(6087,plain,
% 1.41/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s71, s72)) | node7(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s71, s72)) | node7(s71, s72))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6088,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s71, s72)) | node7(s71, s72))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6089,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s71, s72)) | node7(s71, s72)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6088, 6087])).
% 1.41/1.33 tff(6090,plain,
% 1.41/1.33 (node7(s71, s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6089, 206, 6086])).
% 1.41/1.33 tff(6091,plain,
% 1.41/1.33 (((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node7(s71, s72)) | m_main_v_state1(s72, 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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node7(s71, s72)) | m_main_v_state1(s72, c_t1))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6092,plain,
% 1.41/1.33 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node7(s71, s72)) | m_main_v_state1(s72, c_t1))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6093,plain,
% 1.41/1.33 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node7(s71, s72)) | m_main_v_state1(s72, c_t1)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6092, 6091])).
% 1.41/1.33 tff(6094,plain,
% 1.41/1.33 ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | m_main_v_state1(s72, c_t1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6093, 651, 6090])).
% 1.41/1.33 tff(6095,plain,
% 1.41/1.33 (m_main_v_state1(s72, c_t1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6094, 6079, 6023])).
% 1.41/1.33 tff(6096,plain,
% 1.41/1.33 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s72, c_n1)) | (~m_main_v_state1(s72, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s72, c_n1)) | (~m_main_v_state1(s72, c_t1)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6097,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s72, c_n1)) | (~m_main_v_state1(s72, c_t1)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6098,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s72, c_n1)) | (~m_main_v_state1(s72, c_t1))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6097, 6096])).
% 1.41/1.33 tff(6099,plain,
% 1.41/1.33 (~m_main_v_state1(s72, c_n1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6098, 17, 6095])).
% 1.41/1.33 tff(6100,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s72, c_n1) | (~node1(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s72, c_n1) | (~node1(s72)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6101,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s72, c_n1) | (~node1(s72)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6102,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s72, c_n1) | (~node1(s72))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6101, 6100])).
% 1.41/1.33 tff(6103,plain,
% 1.41/1.33 (~node1(s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6102, 421, 6099])).
% 1.41/1.33 tff(6104,plain,
% 1.41/1.33 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s71, s72)) | node18(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s71, s72)) | node18(s71, s72))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6105,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s71, s72)) | node18(s71, s72))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6106,plain,
% 1.41/1.33 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s71, s72)) | node18(s71, s72)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6105, 6104])).
% 1.41/1.33 tff(6107,plain,
% 1.41/1.33 (node18(s71, s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6106, 125, 6086])).
% 1.41/1.33 tff(6108,plain,
% 1.41/1.33 (((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, 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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, c_2))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6109,plain,
% 1.41/1.33 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, c_2))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6110,plain,
% 1.41/1.33 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | (~node18(s71, s72)) | m_main_v_turn(s72, c_2)),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 1.41/1.33 tff(6111,plain,
% 1.41/1.33 ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | m_main_v_turn(s72, c_2)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6110, 760, 6107])).
% 1.41/1.33 tff(6112,plain,
% 1.41/1.33 (m_main_v_turn(s72, c_2)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6111, 6079, 6023])).
% 1.41/1.33 tff(6113,plain,
% 1.41/1.33 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s72, c_1)) | (~m_main_v_turn(s72, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s72, c_1)) | (~m_main_v_turn(s72, c_2)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6114,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s72, c_1)) | (~m_main_v_turn(s72, c_2)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6115,plain,
% 1.41/1.33 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s72, c_1)) | (~m_main_v_turn(s72, c_2))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 1.41/1.33 tff(6116,plain,
% 1.41/1.33 (~m_main_v_turn(s72, c_1)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6115, 156, 6112])).
% 1.41/1.33 tff(6117,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s72, c_1) | (~node5(s72)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s72, c_1) | (~node5(s72)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6118,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s72, c_1) | (~node5(s72)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6119,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s72, c_1) | (~node5(s72))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6118, 6117])).
% 1.41/1.33 tff(6120,plain,
% 1.41/1.33 (~node5(s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6119, 776, 6116])).
% 1.41/1.33 tff(6121,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s72, c_n1) | (~node2(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s72, c_n1) | (~node2(s72)))),
% 1.41/1.33 inference(rewrite,[status(thm)],[])).
% 1.41/1.33 tff(6122,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s72, c_n1) | (~node2(s72)))),
% 1.41/1.33 inference(quant_inst,[status(thm)],[])).
% 1.41/1.33 tff(6123,plain,
% 1.41/1.33 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s72, c_n1) | (~node2(s72))),
% 1.41/1.33 inference(modus_ponens,[status(thm)],[6122, 6121])).
% 1.41/1.33 tff(6124,plain,
% 1.41/1.33 (~node2(s72)),
% 1.41/1.33 inference(unit_resolution,[status(thm)],[6123, 787, 6099])).
% 1.41/1.33 tff(6125,plain,
% 1.41/1.33 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s72, c_n1) | (~node3(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s72, c_n1) | (~node3(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6126,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s72, c_n1) | (~node3(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6127,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s72, c_n1) | (~node3(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6126, 6125])).
% 1.41/1.34 tff(6128,plain,
% 1.41/1.34 (~node3(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6127, 798, 6099])).
% 1.41/1.34 tff(6129,plain,
% 1.41/1.34 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s72, c_t1)) | (~m_main_v_state1(s72, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s72, c_t1)) | (~m_main_v_state1(s72, c_c1)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6130,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s72, c_t1)) | (~m_main_v_state1(s72, c_c1)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6131,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s72, c_t1)) | (~m_main_v_state1(s72, c_c1))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6130, 6129])).
% 1.41/1.34 tff(6132,plain,
% 1.41/1.34 (~m_main_v_state1(s72, c_c1)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6131, 539, 6095])).
% 1.41/1.34 tff(6133,plain,
% 1.41/1.34 (((~![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(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71)))) <=> ((~![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(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6134,plain,
% 1.41/1.34 (((~node13(s70, s71)) | m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, c_n2))) <=> (m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6135,plain,
% 1.41/1.34 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s70, s71)) | m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, 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(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71))))),
% 1.41/1.34 inference(monotonicity,[status(thm)],[6134])).
% 1.41/1.34 tff(6136,plain,
% 1.41/1.34 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s70, s71)) | m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, 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(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71)))),
% 1.41/1.34 inference(transitivity,[status(thm)],[6135, 6133])).
% 1.41/1.34 tff(6137,plain,
% 1.41/1.34 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s70, s71)) | m_main_v_state2(s70, c_n2) | (~m_main_v_state2(s71, c_n2)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6138,plain,
% 1.41/1.34 ((~![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(s70, c_n2) | (~m_main_v_state2(s71, c_n2)) | (~node13(s70, s71))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6137, 6136])).
% 1.41/1.34 tff(6139,plain,
% 1.41/1.34 (~m_main_v_state2(s71, c_n2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6138, 311, 5980, 6072])).
% 1.41/1.34 tff(6140,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s71, c_n2) | (~node9(s71)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s71, c_n2) | (~node9(s71)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6141,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s71, c_n2) | (~node9(s71)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6142,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s71, c_n2) | (~node9(s71))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 1.41/1.34 tff(6143,plain,
% 1.41/1.34 (~node9(s71)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6142, 88, 6139])).
% 1.41/1.34 tff(6144,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s71, c_n2) | (~node10(s71)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s71, c_n2) | (~node10(s71)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6145,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s71, c_n2) | (~node10(s71)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6146,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s71, c_n2) | (~node10(s71))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6145, 6144])).
% 1.41/1.34 tff(6147,plain,
% 1.41/1.34 (~node10(s71)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6146, 249, 6139])).
% 1.41/1.34 tff(6148,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s71, c_n2) | (~node8(s71)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s71, c_n2) | (~node8(s71)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6149,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s71, c_n2) | (~node8(s71)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6150,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s71, c_n2) | (~node8(s71))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6149, 6148])).
% 1.41/1.34 tff(6151,plain,
% 1.41/1.34 (~node8(s71)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6150, 271, 6139])).
% 1.41/1.34 tff(6152,plain,
% 1.41/1.34 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s71, s72)) | node14(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s71, s72)) | node14(s71, s72))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6153,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s71, s72)) | node14(s71, s72))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6154,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s71, s72)) | node14(s71, s72)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6153, 6152])).
% 1.41/1.34 tff(6155,plain,
% 1.41/1.34 (node14(s71, s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6154, 7, 6086])).
% 1.41/1.34 tff(6156,plain,
% 1.41/1.34 (((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | node9(s71) | node8(s71) | node10(s71) | (~node14(s71, s72)) | m_main_v_state2(s72, 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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | node9(s71) | node8(s71) | node10(s71) | (~node14(s71, s72)) | m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6157,plain,
% 1.41/1.34 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | node9(s71) | node8(s71) | node10(s71) | (~node14(s71, s72)) | m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6158,plain,
% 1.41/1.34 ((~![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(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | node9(s71) | node8(s71) | node10(s71) | (~node14(s71, s72)) | m_main_v_state2(s72, c_c2)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 1.41/1.34 tff(6159,plain,
% 1.41/1.34 ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state2(s71, c_t2)) | node9(s71) | node8(s71) | node10(s71) | m_main_v_state2(s72, c_c2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6158, 617, 6155])).
% 1.41/1.34 tff(6160,plain,
% 1.41/1.34 (m_main_v_state2(s72, c_c2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6159, 6151, 6023, 6079, 6147, 6143])).
% 1.41/1.34 tff(6161,plain,
% 1.41/1.34 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s72, c_n2)) | (~m_main_v_state2(s72, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s72, c_n2)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6162,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s72, c_n2)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6163,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s72, c_n2)) | (~m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6162, 6161])).
% 1.41/1.34 tff(6164,plain,
% 1.41/1.34 (~m_main_v_state2(s72, c_n2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6163, 697, 6160])).
% 1.41/1.34 tff(6165,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s72, c_n2) | (~node4(s72)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s72, c_n2) | (~node4(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6166,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s72, c_n2) | (~node4(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6167,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s72, c_n2) | (~node4(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 1.41/1.34 tff(6168,plain,
% 1.41/1.34 (~node4(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6167, 388, 6164])).
% 1.41/1.34 tff(6169,plain,
% 1.41/1.34 (succ(s72, s73) <=> succ(s72, s73)),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6170,axiom,(succ(s72, s73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound73')).
% 1.41/1.34 tff(6171,plain,
% 1.41/1.34 (succ(s72, s73)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6170, 6169])).
% 1.41/1.34 tff(6172,plain,
% 1.41/1.34 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6173,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6174,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 1.41/1.34 tff(6175,plain,
% 1.41/1.34 (trans(s72, s73)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6174, 6171, 39])).
% 1.41/1.34 tff(6176,plain,
% 1.41/1.34 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s72, s73)) | node7(s72, s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s72, s73)) | node7(s72, s73))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6177,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s72, s73)) | node7(s72, s73))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6178,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s72, s73)) | node7(s72, s73)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6177, 6176])).
% 1.41/1.34 tff(6179,plain,
% 1.41/1.34 (node7(s72, s73)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6178, 206, 6175])).
% 1.41/1.34 tff(6180,plain,
% 1.41/1.34 (((~![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(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73) | (~node7(s72, s73)))) <=> ((~![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(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73) | (~node7(s72, s73)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6181,plain,
% 1.41/1.34 ((~![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(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73) | (~node7(s72, s73)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6182,plain,
% 1.41/1.34 ((~![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(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73) | (~node7(s72, s73))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.41/1.34 tff(6183,plain,
% 1.41/1.34 (m_main_v_state1(s72, c_c1) | node1(s72) | node2(s72) | node3(s72) | node4(s72) | node5(s72) | node6(s72, s73)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6182, 820, 6179])).
% 1.41/1.34 tff(6184,plain,
% 1.41/1.34 (node6(s72, s73)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6183, 6168, 6132, 6128, 6124, 6120, 6103])).
% 1.41/1.34 tff(6185,plain,
% 1.41/1.34 (((~![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(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73)))) <=> ((~![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(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6186,plain,
% 1.41/1.34 (((~node6(s72, s73)) | (~m_main_v_state1(s72, c_t1)) | m_main_v_state1(s73, c_t1)) <=> ((~m_main_v_state1(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6187,plain,
% 1.41/1.34 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s72, s73)) | (~m_main_v_state1(s72, c_t1)) | m_main_v_state1(s73, 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(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73))))),
% 1.41/1.34 inference(monotonicity,[status(thm)],[6186])).
% 1.41/1.34 tff(6188,plain,
% 1.41/1.34 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s72, s73)) | (~m_main_v_state1(s72, c_t1)) | m_main_v_state1(s73, 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(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73)))),
% 1.41/1.34 inference(transitivity,[status(thm)],[6187, 6185])).
% 1.41/1.34 tff(6189,plain,
% 1.41/1.34 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s72, s73)) | (~m_main_v_state1(s72, c_t1)) | m_main_v_state1(s73, c_t1))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6190,plain,
% 1.41/1.34 ((~![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(s72, c_t1)) | m_main_v_state1(s73, c_t1) | (~node6(s72, s73))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6189, 6188])).
% 1.41/1.34 tff(6191,plain,
% 1.41/1.34 (m_main_v_state1(s73, c_t1)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6190, 856, 6095, 6184])).
% 1.41/1.34 tff(6192,plain,
% 1.41/1.34 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s72, c_t2)) | (~m_main_v_state2(s72, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s72, c_t2)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6193,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s72, c_t2)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6194,plain,
% 1.41/1.34 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s72, c_t2)) | (~m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 1.41/1.34 tff(6195,plain,
% 1.41/1.34 (~m_main_v_state2(s72, c_t2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6194, 260, 6160])).
% 1.41/1.34 tff(6196,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s72, c_t2) | (~node12(s72)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s72, c_t2) | (~node12(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6197,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s72, c_t2) | (~node12(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6198,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s72, c_t2) | (~node12(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6197, 6196])).
% 1.41/1.34 tff(6199,plain,
% 1.41/1.34 (~node12(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6198, 633, 6195])).
% 1.41/1.34 tff(6200,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s72, c_n1) | (~node11(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s72, c_n1) | (~node11(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6201,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s72, c_n1) | (~node11(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6202,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s72, c_n1) | (~node11(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6201, 6200])).
% 1.41/1.34 tff(6203,plain,
% 1.41/1.34 (~node11(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6202, 238, 6099])).
% 1.41/1.34 tff(6204,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s72, c_c1) | (~node10(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s72, c_c1) | (~node10(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6205,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s72, c_c1) | (~node10(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6206,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s72, c_c1) | (~node10(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6205, 6204])).
% 1.41/1.34 tff(6207,plain,
% 1.41/1.34 (~node10(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6206, 675, 6132])).
% 1.41/1.34 tff(6208,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s72, c_n1) | (~node9(s72)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s72, c_n1) | (~node9(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6209,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s72, c_n1) | (~node9(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6210,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s72, c_n1) | (~node9(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6209, 6208])).
% 1.41/1.34 tff(6211,plain,
% 1.41/1.34 (~node9(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6210, 686, 6099])).
% 1.41/1.34 tff(6212,plain,
% 1.41/1.34 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s72, c_n2) | (~node8(s72)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s72, c_n2) | (~node8(s72)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6213,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s72, c_n2) | (~node8(s72)))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6214,plain,
% 1.41/1.34 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s72, c_n2) | (~node8(s72))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6213, 6212])).
% 1.41/1.34 tff(6215,plain,
% 1.41/1.34 (~node8(s72)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6214, 271, 6164])).
% 1.41/1.34 tff(6216,plain,
% 1.41/1.34 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s72, s73)) | node14(s72, s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s72, s73)) | node14(s72, s73))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6217,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s72, s73)) | node14(s72, s73))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6218,plain,
% 1.41/1.34 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s72, s73)) | node14(s72, s73)),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6217, 6216])).
% 1.41/1.34 tff(6219,plain,
% 1.41/1.34 (node14(s72, s73)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6218, 7, 6175])).
% 1.41/1.34 tff(6220,plain,
% 1.41/1.34 (((~![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(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, 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(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6221,plain,
% 1.41/1.34 (((~m_main_v_state2(s72, c_c2)) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | m_main_v_state2(s73, c_n2)) <=> (m_main_v_state2(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(rewrite,[status(thm)],[])).
% 1.41/1.34 tff(6222,plain,
% 1.41/1.34 (((~![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(s72, c_c2)) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | m_main_v_state2(s73, 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(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, c_c2))))),
% 1.41/1.34 inference(monotonicity,[status(thm)],[6221])).
% 1.41/1.34 tff(6223,plain,
% 1.41/1.34 (((~![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(s72, c_c2)) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | m_main_v_state2(s73, 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(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, c_c2)))),
% 1.41/1.34 inference(transitivity,[status(thm)],[6222, 6220])).
% 1.41/1.34 tff(6224,plain,
% 1.41/1.34 ((~![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(s72, c_c2)) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | m_main_v_state2(s73, c_n2))),
% 1.41/1.34 inference(quant_inst,[status(thm)],[])).
% 1.41/1.34 tff(6225,plain,
% 1.41/1.34 ((~![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(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~node14(s72, s73)) | (~m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 1.41/1.34 tff(6226,plain,
% 1.41/1.34 (m_main_v_state2(s73, c_n2) | node9(s72) | node8(s72) | node10(s72) | node11(s72) | node12(s72) | (~m_main_v_state2(s72, c_c2))),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6225, 726, 6219])).
% 1.41/1.34 tff(6227,plain,
% 1.41/1.34 (m_main_v_state2(s73, c_n2)),
% 1.41/1.34 inference(unit_resolution,[status(thm)],[6226, 6215, 6160, 6211, 6207, 6203, 6199])).
% 1.41/1.34 tff(6228,plain,
% 1.41/1.34 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_t2)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6229,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_t2)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6230,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_t2))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6229, 6228])).
% 1.41/1.35 tff(6231,plain,
% 1.41/1.35 (~m_main_v_state2(s73, c_t2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6230, 77, 6227])).
% 1.41/1.35 tff(6232,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s73, c_t2) | (~node15(s73)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s73, c_t2) | (~node15(s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6233,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s73, c_t2) | (~node15(s73)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6234,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s73, c_t2) | (~node15(s73))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6233, 6232])).
% 1.41/1.35 tff(6235,plain,
% 1.41/1.35 (~node15(s73)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6234, 103, 6231])).
% 1.41/1.35 tff(6236,plain,
% 1.41/1.35 (succ(s73, s74) <=> succ(s73, s74)),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6237,axiom,(succ(s73, s74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound74')).
% 1.41/1.35 tff(6238,plain,
% 1.41/1.35 (succ(s73, s74)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 1.41/1.35 tff(6239,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6240,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6241,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6240, 6239])).
% 1.41/1.35 tff(6242,plain,
% 1.41/1.35 (trans(s73, s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6241, 6238, 39])).
% 1.41/1.35 tff(6243,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s73, s74)) | node18(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s73, s74)) | node18(s73, s74))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6244,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s73, s74)) | node18(s73, s74))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6245,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s73, s74)) | node18(s73, s74)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6244, 6243])).
% 1.41/1.35 tff(6246,plain,
% 1.41/1.35 (node18(s73, s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6245, 125, 6242])).
% 1.41/1.35 tff(6247,plain,
% 1.41/1.35 (((~![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(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, 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(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6248,plain,
% 1.41/1.35 (((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node15(s73) | (~node18(s73, s74)) | m_main_v_turn(s74, c_1)) <=> (node15(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6249,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node15(s73) | (~node18(s73, s74)) | m_main_v_turn(s74, 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(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1)))),
% 1.41/1.35 inference(monotonicity,[status(thm)],[6248])).
% 1.41/1.35 tff(6250,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node15(s73) | (~node18(s73, s74)) | m_main_v_turn(s74, 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(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1))),
% 1.41/1.35 inference(transitivity,[status(thm)],[6249, 6247])).
% 1.41/1.35 tff(6251,plain,
% 1.41/1.35 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node15(s73) | (~node18(s73, s74)) | m_main_v_turn(s74, c_1))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6252,plain,
% 1.41/1.35 ((~![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(s73) | (~node18(s73, s74)) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6251, 6250])).
% 1.41/1.35 tff(6253,plain,
% 1.41/1.35 (node15(s73) | (~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_turn(s74, c_1)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6252, 992, 6246])).
% 1.41/1.35 tff(6254,plain,
% 1.41/1.35 (m_main_v_turn(s74, c_1)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6253, 6235, 6227, 6191])).
% 1.41/1.35 tff(6255,plain,
% 1.41/1.35 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s74, c_1)) | (~m_main_v_turn(s74, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s74, c_1)) | (~m_main_v_turn(s74, c_2)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6256,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s74, c_1)) | (~m_main_v_turn(s74, c_2)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6257,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s74, c_1)) | (~m_main_v_turn(s74, c_2))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6256, 6255])).
% 1.41/1.35 tff(6258,plain,
% 1.41/1.35 (~m_main_v_turn(s74, c_2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6257, 156, 6254])).
% 1.41/1.35 tff(6259,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s74, c_2) | (~node12(s74)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s74, c_2) | (~node12(s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6260,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s74, c_2) | (~node12(s74)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6261,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s74, c_2) | (~node12(s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 1.41/1.35 tff(6262,plain,
% 1.41/1.35 (~node12(s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6261, 184, 6258])).
% 1.41/1.35 tff(6263,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s73, s74)) | node14(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s73, s74)) | node14(s73, s74))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6264,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s73, s74)) | node14(s73, s74))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6265,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s73, s74)) | node14(s73, s74)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6264, 6263])).
% 1.41/1.35 tff(6266,plain,
% 1.41/1.35 (node14(s73, s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6265, 7, 6242])).
% 1.41/1.35 tff(6267,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | (~node14(s73, s74)) | m_main_v_state2(s74, 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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | (~node14(s73, s74)) | m_main_v_state2(s74, c_t2))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6268,plain,
% 1.41/1.35 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | (~node14(s73, s74)) | m_main_v_state2(s74, c_t2))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6269,plain,
% 1.41/1.35 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | (~node14(s73, s74)) | m_main_v_state2(s74, c_t2)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6268, 6267])).
% 1.41/1.35 tff(6270,plain,
% 1.41/1.35 ((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state2(s74, c_t2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6269, 922, 6266])).
% 1.41/1.35 tff(6271,plain,
% 1.41/1.35 (m_main_v_state2(s74, c_t2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6270, 6191, 6227])).
% 1.41/1.35 tff(6272,plain,
% 1.41/1.35 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s74, c_n2)) | (~m_main_v_state2(s74, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s74, c_n2)) | (~m_main_v_state2(s74, c_t2)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6273,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s74, c_n2)) | (~m_main_v_state2(s74, c_t2)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6274,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s74, c_n2)) | (~m_main_v_state2(s74, c_t2))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6273, 6272])).
% 1.41/1.35 tff(6275,plain,
% 1.41/1.35 (~m_main_v_state2(s74, c_n2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6274, 77, 6271])).
% 1.41/1.35 tff(6276,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s74, c_n2) | (~node8(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s74, c_n2) | (~node8(s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6277,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s74, c_n2) | (~node8(s74)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6278,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s74, c_n2) | (~node8(s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6277, 6276])).
% 1.41/1.35 tff(6279,plain,
% 1.41/1.35 (~node8(s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6278, 271, 6275])).
% 1.41/1.35 tff(6280,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s74, c_n2) | (~node9(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s74, c_n2) | (~node9(s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6281,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s74, c_n2) | (~node9(s74)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6282,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s74, c_n2) | (~node9(s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6281, 6280])).
% 1.41/1.35 tff(6283,plain,
% 1.41/1.35 (~node9(s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6282, 88, 6275])).
% 1.41/1.35 tff(6284,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s74, c_n2) | (~node10(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s74, c_n2) | (~node10(s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6285,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s74, c_n2) | (~node10(s74)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6286,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s74, c_n2) | (~node10(s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6285, 6284])).
% 1.41/1.35 tff(6287,plain,
% 1.41/1.35 (~node10(s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6286, 249, 6275])).
% 1.41/1.35 tff(6288,plain,
% 1.41/1.35 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s74, c_t2)) | (~m_main_v_state2(s74, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s74, c_t2)) | (~m_main_v_state2(s74, c_c2)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6289,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s74, c_t2)) | (~m_main_v_state2(s74, c_c2)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6290,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s74, c_t2)) | (~m_main_v_state2(s74, c_c2))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6289, 6288])).
% 1.41/1.35 tff(6291,plain,
% 1.41/1.35 (~m_main_v_state2(s74, c_c2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6290, 260, 6271])).
% 1.41/1.35 tff(6292,plain,
% 1.41/1.35 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_c2)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6293,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_c2)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6294,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s73, c_n2)) | (~m_main_v_state2(s73, c_c2))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6293, 6292])).
% 1.41/1.35 tff(6295,plain,
% 1.41/1.35 (~m_main_v_state2(s73, c_c2)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6294, 697, 6227])).
% 1.41/1.35 tff(6296,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s73, c_c2) | (~node3(s73)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s73, c_c2) | (~node3(s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6297,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s73, c_c2) | (~node3(s73)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6298,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s73, c_c2) | (~node3(s73))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6297, 6296])).
% 1.41/1.35 tff(6299,plain,
% 1.41/1.35 (~node3(s73)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6298, 399, 6295])).
% 1.41/1.35 tff(6300,plain,
% 1.41/1.35 (((~![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(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73)))) <=> ((~![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(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6301,plain,
% 1.41/1.35 (((~node6(s72, s73)) | m_main_v_state1(s72, c_n1) | (~m_main_v_state1(s73, c_n1))) <=> (m_main_v_state1(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6302,plain,
% 1.41/1.35 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s72, s73)) | m_main_v_state1(s72, c_n1) | (~m_main_v_state1(s73, 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(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73))))),
% 1.41/1.35 inference(monotonicity,[status(thm)],[6301])).
% 1.41/1.35 tff(6303,plain,
% 1.41/1.35 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s72, s73)) | m_main_v_state1(s72, c_n1) | (~m_main_v_state1(s73, 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(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73)))),
% 1.41/1.35 inference(transitivity,[status(thm)],[6302, 6300])).
% 1.41/1.35 tff(6304,plain,
% 1.41/1.35 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s72, s73)) | m_main_v_state1(s72, c_n1) | (~m_main_v_state1(s73, c_n1)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6305,plain,
% 1.41/1.35 ((~![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(s72, c_n1) | (~m_main_v_state1(s73, c_n1)) | (~node6(s72, s73))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 1.41/1.35 tff(6306,plain,
% 1.41/1.35 (~m_main_v_state1(s73, c_n1)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6305, 835, 6099, 6184])).
% 1.41/1.35 tff(6307,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s73, c_n1) | (~node2(s73)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s73, c_n1) | (~node2(s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6308,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s73, c_n1) | (~node2(s73)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6309,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s73, c_n1) | (~node2(s73))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.41/1.35 tff(6310,plain,
% 1.41/1.35 (~node2(s73)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6309, 787, 6306])).
% 1.41/1.35 tff(6311,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s73, c_t2) | (~node1(s73)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s73, c_t2) | (~node1(s73)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6312,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s73, c_t2) | (~node1(s73)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6313,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s73, c_t2) | (~node1(s73))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 1.41/1.35 tff(6314,plain,
% 1.41/1.35 (~node1(s73)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6313, 195, 6231])).
% 1.41/1.35 tff(6315,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s73, s74)) | node7(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s73, s74)) | node7(s73, s74))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6316,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s73, s74)) | node7(s73, s74))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6317,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s73, s74)) | node7(s73, s74)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.41/1.35 tff(6318,plain,
% 1.41/1.35 (node7(s73, s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6317, 206, 6242])).
% 1.41/1.35 tff(6319,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)))) <=> ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6320,plain,
% 1.41/1.35 (((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)) | m_main_v_state1(s74, c_c1)) <=> ((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6321,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)) | m_main_v_state1(s74, 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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74))))),
% 1.41/1.35 inference(monotonicity,[status(thm)],[6320])).
% 1.41/1.35 tff(6322,plain,
% 1.41/1.35 (((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)) | m_main_v_state1(s74, 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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)))),
% 1.41/1.35 inference(transitivity,[status(thm)],[6321, 6319])).
% 1.41/1.35 tff(6323,plain,
% 1.41/1.35 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74)) | m_main_v_state1(s74, c_c1))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6324,plain,
% 1.41/1.35 ((~![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(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73) | (~node7(s73, s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 1.41/1.35 tff(6325,plain,
% 1.41/1.35 ((~m_main_v_state1(s73, c_t1)) | (~m_main_v_state2(s73, c_n2)) | m_main_v_state1(s74, c_c1) | node1(s73) | node2(s73) | node3(s73)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6324, 892, 6318])).
% 1.41/1.35 tff(6326,plain,
% 1.41/1.35 (m_main_v_state1(s74, c_c1)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6325, 6314, 6227, 6191, 6310, 6299])).
% 1.41/1.35 tff(6327,plain,
% 1.41/1.35 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s74, c_n1)) | (~m_main_v_state1(s74, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s74, c_n1)) | (~m_main_v_state1(s74, c_c1)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6328,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s74, c_n1)) | (~m_main_v_state1(s74, c_c1)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6329,plain,
% 1.41/1.35 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s74, c_n1)) | (~m_main_v_state1(s74, c_c1))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6328, 6327])).
% 1.41/1.35 tff(6330,plain,
% 1.41/1.35 (~m_main_v_state1(s74, c_n1)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6329, 454, 6326])).
% 1.41/1.35 tff(6331,plain,
% 1.41/1.35 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s74, c_n1) | (~node11(s74)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s74, c_n1) | (~node11(s74)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6332,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s74, c_n1) | (~node11(s74)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6333,plain,
% 1.41/1.35 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s74, c_n1) | (~node11(s74))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 1.41/1.35 tff(6334,plain,
% 1.41/1.35 (~node11(s74)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6333, 238, 6330])).
% 1.41/1.35 tff(6335,plain,
% 1.41/1.35 (succ(s74, s75) <=> succ(s74, s75)),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6336,axiom,(succ(s74, s75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound75')).
% 1.41/1.35 tff(6337,plain,
% 1.41/1.35 (succ(s74, s75)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6336, 6335])).
% 1.41/1.35 tff(6338,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6339,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6340,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6339, 6338])).
% 1.41/1.35 tff(6341,plain,
% 1.41/1.35 (trans(s74, s75)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6340, 6337, 39])).
% 1.41/1.35 tff(6342,plain,
% 1.41/1.35 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s74, s75)) | node14(s74, s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s74, s75)) | node14(s74, s75))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6343,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s74, s75)) | node14(s74, s75))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6344,plain,
% 1.41/1.35 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s74, s75)) | node14(s74, s75)),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 1.41/1.35 tff(6345,plain,
% 1.41/1.35 (node14(s74, s75)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6344, 7, 6341])).
% 1.41/1.35 tff(6346,plain,
% 1.41/1.35 (((~![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(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75) | (~node14(s74, s75)))) <=> ((~![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(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75) | (~node14(s74, s75)))),
% 1.41/1.35 inference(rewrite,[status(thm)],[])).
% 1.41/1.35 tff(6347,plain,
% 1.41/1.35 ((~![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(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75) | (~node14(s74, s75)))),
% 1.41/1.35 inference(quant_inst,[status(thm)],[])).
% 1.41/1.35 tff(6348,plain,
% 1.41/1.35 ((~![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(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75) | (~node14(s74, s75))),
% 1.41/1.35 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 1.41/1.35 tff(6349,plain,
% 1.41/1.35 (m_main_v_state2(s74, c_c2) | node9(s74) | node8(s74) | node10(s74) | node11(s74) | node12(s74) | node13(s74, s75)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6348, 296, 6345])).
% 1.41/1.35 tff(6350,plain,
% 1.41/1.35 (node13(s74, s75)),
% 1.41/1.35 inference(unit_resolution,[status(thm)],[6349, 6334, 6291, 6287, 6283, 6279, 6262])).
% 1.41/1.35 tff(6351,plain,
% 1.41/1.35 (((~![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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75)))) <=> ((~![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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6352,plain,
% 1.41/1.36 (((~node13(s74, s75)) | m_main_v_state2(s74, c_n2) | (~m_main_v_state2(s75, c_n2))) <=> (m_main_v_state2(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6353,plain,
% 1.41/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s74, s75)) | m_main_v_state2(s74, c_n2) | (~m_main_v_state2(s75, 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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75))))),
% 1.41/1.36 inference(monotonicity,[status(thm)],[6352])).
% 1.41/1.36 tff(6354,plain,
% 1.41/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s74, s75)) | m_main_v_state2(s74, c_n2) | (~m_main_v_state2(s75, 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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75)))),
% 1.41/1.36 inference(transitivity,[status(thm)],[6353, 6351])).
% 1.41/1.36 tff(6355,plain,
% 1.41/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s74, s75)) | m_main_v_state2(s74, c_n2) | (~m_main_v_state2(s75, c_n2)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6356,plain,
% 1.41/1.36 ((~![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(s74, c_n2) | (~m_main_v_state2(s75, c_n2)) | (~node13(s74, s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6355, 6354])).
% 1.41/1.36 tff(6357,plain,
% 1.41/1.36 (~m_main_v_state2(s75, c_n2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6356, 311, 6275, 6350])).
% 1.41/1.36 tff(6358,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s75, c_n2) | (~node9(s75)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s75, c_n2) | (~node9(s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6359,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s75, c_n2) | (~node9(s75)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6360,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s75, c_n2) | (~node9(s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6359, 6358])).
% 1.41/1.36 tff(6361,plain,
% 1.41/1.36 (~node9(s75)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6360, 88, 6357])).
% 1.41/1.36 tff(6362,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s75, c_n2) | (~node10(s75)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s75, c_n2) | (~node10(s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6363,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s75, c_n2) | (~node10(s75)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6364,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s75, c_n2) | (~node10(s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6363, 6362])).
% 1.41/1.36 tff(6365,plain,
% 1.41/1.36 (~node10(s75)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6364, 249, 6357])).
% 1.41/1.36 tff(6366,plain,
% 1.41/1.36 (((~![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(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75)))) <=> ((~![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(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6367,plain,
% 1.41/1.36 (((~node13(s74, s75)) | (~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, c_t2)) <=> ((~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6368,plain,
% 1.41/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s74, s75)) | (~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, 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(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75))))),
% 1.41/1.36 inference(monotonicity,[status(thm)],[6367])).
% 1.41/1.36 tff(6369,plain,
% 1.41/1.36 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s74, s75)) | (~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, 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(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75)))),
% 1.41/1.36 inference(transitivity,[status(thm)],[6368, 6366])).
% 1.41/1.36 tff(6370,plain,
% 1.41/1.36 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s74, s75)) | (~m_main_v_state2(s74, c_t2)) | m_main_v_state2(s75, c_t2))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6371,plain,
% 1.41/1.36 ((~![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(s74, c_t2)) | m_main_v_state2(s75, c_t2) | (~node13(s74, s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6370, 6369])).
% 1.41/1.36 tff(6372,plain,
% 1.41/1.36 (m_main_v_state2(s75, c_t2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6371, 518, 6271, 6350])).
% 1.41/1.36 tff(6373,plain,
% 1.41/1.36 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s74, c_t1)) | (~m_main_v_state1(s74, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s74, c_t1)) | (~m_main_v_state1(s74, c_c1)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6374,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s74, c_t1)) | (~m_main_v_state1(s74, c_c1)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6375,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s74, c_t1)) | (~m_main_v_state1(s74, c_c1))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 1.41/1.36 tff(6376,plain,
% 1.41/1.36 (~m_main_v_state1(s74, c_t1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6375, 539, 6326])).
% 1.41/1.36 tff(6377,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s74, c_t1) | (~node5(s74)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s74, c_t1) | (~node5(s74)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6378,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s74, c_t1) | (~node5(s74)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6379,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s74, c_t1) | (~node5(s74))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6378, 6377])).
% 1.41/1.36 tff(6380,plain,
% 1.41/1.36 (~node5(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6379, 550, 6376])).
% 1.41/1.36 tff(6381,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s74, c_n2) | (~node4(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s74, c_n2) | (~node4(s74)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6382,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s74, c_n2) | (~node4(s74)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6383,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s74, c_n2) | (~node4(s74))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6382, 6381])).
% 1.41/1.36 tff(6384,plain,
% 1.41/1.36 (~node4(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6383, 388, 6275])).
% 1.41/1.36 tff(6385,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s74, c_c2) | (~node3(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s74, c_c2) | (~node3(s74)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6386,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s74, c_c2) | (~node3(s74)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6387,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s74, c_c2) | (~node3(s74))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6386, 6385])).
% 1.41/1.36 tff(6388,plain,
% 1.41/1.36 (~node3(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6387, 399, 6291])).
% 1.41/1.36 tff(6389,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s74, c_n2) | (~node2(s74)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s74, c_n2) | (~node2(s74)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6390,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s74, c_n2) | (~node2(s74)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6391,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s74, c_n2) | (~node2(s74))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6390, 6389])).
% 1.41/1.36 tff(6392,plain,
% 1.41/1.36 (~node2(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6391, 410, 6275])).
% 1.41/1.36 tff(6393,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s74, c_n1) | (~node1(s74)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s74, c_n1) | (~node1(s74)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6394,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s74, c_n1) | (~node1(s74)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6395,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s74, c_n1) | (~node1(s74))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6394, 6393])).
% 1.41/1.36 tff(6396,plain,
% 1.41/1.36 (~node1(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6395, 421, 6330])).
% 1.41/1.36 tff(6397,plain,
% 1.41/1.36 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s74, s75)) | node7(s74, s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s74, s75)) | node7(s74, s75))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6398,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s74, s75)) | node7(s74, s75))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6399,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s74, s75)) | node7(s74, s75)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6398, 6397])).
% 1.41/1.36 tff(6400,plain,
% 1.41/1.36 (node7(s74, s75)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6399, 206, 6341])).
% 1.41/1.36 tff(6401,plain,
% 1.41/1.36 (((~![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(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)))) <=> ((~![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(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6402,plain,
% 1.41/1.36 (((~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)) | m_main_v_state1(s75, c_n1)) <=> (m_main_v_state1(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6403,plain,
% 1.41/1.36 (((~![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(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)) | m_main_v_state1(s75, 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(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75))))),
% 1.41/1.36 inference(monotonicity,[status(thm)],[6402])).
% 1.41/1.36 tff(6404,plain,
% 1.41/1.36 (((~![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(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)) | m_main_v_state1(s75, 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(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)))),
% 1.41/1.36 inference(transitivity,[status(thm)],[6403, 6401])).
% 1.41/1.36 tff(6405,plain,
% 1.41/1.36 ((~![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(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75)) | m_main_v_state1(s75, c_n1))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6406,plain,
% 1.41/1.36 ((~![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(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74) | (~node7(s74, s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 1.41/1.36 tff(6407,plain,
% 1.41/1.36 (m_main_v_state1(s75, c_n1) | (~m_main_v_state1(s74, c_c1)) | node1(s74) | node2(s74) | node3(s74) | node4(s74) | node5(s74)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6406, 584, 6400])).
% 1.41/1.36 tff(6408,plain,
% 1.41/1.36 (m_main_v_state1(s75, c_n1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6407, 6396, 6326, 6392, 6388, 6384, 6380])).
% 1.41/1.36 tff(6409,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s75, c_n2) | (~node8(s75)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s75, c_n2) | (~node8(s75)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6410,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s75, c_n2) | (~node8(s75)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6411,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s75, c_n2) | (~node8(s75))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6410, 6409])).
% 1.41/1.36 tff(6412,plain,
% 1.41/1.36 (~node8(s75)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6411, 271, 6357])).
% 1.41/1.36 tff(6413,plain,
% 1.41/1.36 (succ(s75, s76) <=> succ(s75, s76)),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6414,axiom,(succ(s75, s76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound76')).
% 1.41/1.36 tff(6415,plain,
% 1.41/1.36 (succ(s75, s76)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6414, 6413])).
% 1.41/1.36 tff(6416,plain,
% 1.41/1.36 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6417,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6418,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6417, 6416])).
% 1.41/1.36 tff(6419,plain,
% 1.41/1.36 (trans(s75, s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6418, 6415, 39])).
% 1.41/1.36 tff(6420,plain,
% 1.41/1.36 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s75, s76)) | node14(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s75, s76)) | node14(s75, s76))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6421,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s75, s76)) | node14(s75, s76))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6422,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s75, s76)) | node14(s75, s76)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6421, 6420])).
% 1.41/1.36 tff(6423,plain,
% 1.41/1.36 (node14(s75, s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6422, 7, 6419])).
% 1.41/1.36 tff(6424,plain,
% 1.41/1.36 (((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | node9(s75) | node8(s75) | node10(s75) | (~node14(s75, s76)) | m_main_v_state2(s76, 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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | node9(s75) | node8(s75) | node10(s75) | (~node14(s75, s76)) | m_main_v_state2(s76, c_c2))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6425,plain,
% 1.41/1.36 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | node9(s75) | node8(s75) | node10(s75) | (~node14(s75, s76)) | m_main_v_state2(s76, c_c2))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6426,plain,
% 1.41/1.36 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | node9(s75) | node8(s75) | node10(s75) | (~node14(s75, s76)) | m_main_v_state2(s76, c_c2)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6425, 6424])).
% 1.41/1.36 tff(6427,plain,
% 1.41/1.36 ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | node9(s75) | node8(s75) | node10(s75) | m_main_v_state2(s76, c_c2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6426, 617, 6423])).
% 1.41/1.36 tff(6428,plain,
% 1.41/1.36 (m_main_v_state2(s76, c_c2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6427, 6412, 6408, 6372, 6365, 6361])).
% 1.41/1.36 tff(6429,plain,
% 1.41/1.36 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s76, c_t2)) | (~m_main_v_state2(s76, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s76, c_t2)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6430,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s76, c_t2)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6431,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s76, c_t2)) | (~m_main_v_state2(s76, c_c2))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6430, 6429])).
% 1.41/1.36 tff(6432,plain,
% 1.41/1.36 (~m_main_v_state2(s76, c_t2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6431, 260, 6428])).
% 1.41/1.36 tff(6433,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s76, c_t2) | (~node12(s76)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s76, c_t2) | (~node12(s76)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6434,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s76, c_t2) | (~node12(s76)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6435,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s76, c_t2) | (~node12(s76))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6434, 6433])).
% 1.41/1.36 tff(6436,plain,
% 1.41/1.36 (~node12(s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6435, 633, 6432])).
% 1.41/1.36 tff(6437,plain,
% 1.41/1.36 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s75, s76)) | node7(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s75, s76)) | node7(s75, s76))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6438,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s75, s76)) | node7(s75, s76))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6439,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s75, s76)) | node7(s75, s76)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6438, 6437])).
% 1.41/1.36 tff(6440,plain,
% 1.41/1.36 (node7(s75, s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6439, 206, 6419])).
% 1.41/1.36 tff(6441,plain,
% 1.41/1.36 (((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node7(s75, s76)) | m_main_v_state1(s76, 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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node7(s75, s76)) | m_main_v_state1(s76, c_t1))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6442,plain,
% 1.41/1.36 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node7(s75, s76)) | m_main_v_state1(s76, c_t1))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6443,plain,
% 1.41/1.36 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node7(s75, s76)) | m_main_v_state1(s76, c_t1)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6442, 6441])).
% 1.41/1.36 tff(6444,plain,
% 1.41/1.36 ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | m_main_v_state1(s76, c_t1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6443, 651, 6440])).
% 1.41/1.36 tff(6445,plain,
% 1.41/1.36 (m_main_v_state1(s76, c_t1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6444, 6372, 6408])).
% 1.41/1.36 tff(6446,plain,
% 1.41/1.36 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s76, c_n1)) | (~m_main_v_state1(s76, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s76, c_n1)) | (~m_main_v_state1(s76, c_t1)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6447,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s76, c_n1)) | (~m_main_v_state1(s76, c_t1)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6448,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s76, c_n1)) | (~m_main_v_state1(s76, c_t1))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6447, 6446])).
% 1.41/1.36 tff(6449,plain,
% 1.41/1.36 (~m_main_v_state1(s76, c_n1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6448, 17, 6445])).
% 1.41/1.36 tff(6450,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s76, c_n1) | (~node11(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s76, c_n1) | (~node11(s76)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6451,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s76, c_n1) | (~node11(s76)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6452,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s76, c_n1) | (~node11(s76))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6451, 6450])).
% 1.41/1.36 tff(6453,plain,
% 1.41/1.36 (~node11(s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6452, 238, 6449])).
% 1.41/1.36 tff(6454,plain,
% 1.41/1.36 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s76, c_t1)) | (~m_main_v_state1(s76, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s76, c_t1)) | (~m_main_v_state1(s76, c_c1)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6455,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s76, c_t1)) | (~m_main_v_state1(s76, c_c1)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6456,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s76, c_t1)) | (~m_main_v_state1(s76, c_c1))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6455, 6454])).
% 1.41/1.36 tff(6457,plain,
% 1.41/1.36 (~m_main_v_state1(s76, c_c1)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6456, 539, 6445])).
% 1.41/1.36 tff(6458,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s76, c_c1) | (~node10(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s76, c_c1) | (~node10(s76)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6459,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s76, c_c1) | (~node10(s76)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6460,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s76, c_c1) | (~node10(s76))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6459, 6458])).
% 1.41/1.36 tff(6461,plain,
% 1.41/1.36 (~node10(s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6460, 675, 6457])).
% 1.41/1.36 tff(6462,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s76, c_n1) | (~node9(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s76, c_n1) | (~node9(s76)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6463,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s76, c_n1) | (~node9(s76)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6464,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s76, c_n1) | (~node9(s76))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 1.41/1.36 tff(6465,plain,
% 1.41/1.36 (~node9(s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6464, 686, 6449])).
% 1.41/1.36 tff(6466,plain,
% 1.41/1.36 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s76, c_n2)) | (~m_main_v_state2(s76, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s76, c_n2)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6467,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s76, c_n2)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6468,plain,
% 1.41/1.36 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s76, c_n2)) | (~m_main_v_state2(s76, c_c2))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6467, 6466])).
% 1.41/1.36 tff(6469,plain,
% 1.41/1.36 (~m_main_v_state2(s76, c_n2)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6468, 697, 6428])).
% 1.41/1.36 tff(6470,plain,
% 1.41/1.36 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s76, c_n2) | (~node8(s76)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s76, c_n2) | (~node8(s76)))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6471,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s76, c_n2) | (~node8(s76)))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.36 tff(6472,plain,
% 1.41/1.36 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s76, c_n2) | (~node8(s76))),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6471, 6470])).
% 1.41/1.36 tff(6473,plain,
% 1.41/1.36 (~node8(s76)),
% 1.41/1.36 inference(unit_resolution,[status(thm)],[6472, 271, 6469])).
% 1.41/1.36 tff(6474,plain,
% 1.41/1.36 (succ(s76, s77) <=> succ(s76, s77)),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6475,axiom,(succ(s76, s77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound77')).
% 1.41/1.36 tff(6476,plain,
% 1.41/1.36 (succ(s76, s77)),
% 1.41/1.36 inference(modus_ponens,[status(thm)],[6475, 6474])).
% 1.41/1.36 tff(6477,plain,
% 1.41/1.36 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77))),
% 1.41/1.36 inference(rewrite,[status(thm)],[])).
% 1.41/1.36 tff(6478,plain,
% 1.41/1.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))),
% 1.41/1.36 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6479,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6478, 6477])).
% 1.41/1.37 tff(6480,plain,
% 1.41/1.37 (trans(s76, s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6479, 6476, 39])).
% 1.41/1.37 tff(6481,plain,
% 1.41/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s76, s77)) | node14(s76, s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s76, s77)) | node14(s76, s77))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6482,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s76, s77)) | node14(s76, s77))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6483,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s76, s77)) | node14(s76, s77)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6482, 6481])).
% 1.41/1.37 tff(6484,plain,
% 1.41/1.37 (node14(s76, s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6483, 7, 6480])).
% 1.41/1.37 tff(6485,plain,
% 1.41/1.37 (((~![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(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, 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(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6486,plain,
% 1.41/1.37 (((~m_main_v_state2(s76, c_c2)) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | m_main_v_state2(s77, c_n2)) <=> (m_main_v_state2(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6487,plain,
% 1.41/1.37 (((~![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(s76, c_c2)) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | m_main_v_state2(s77, 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(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2))))),
% 1.41/1.37 inference(monotonicity,[status(thm)],[6486])).
% 1.41/1.37 tff(6488,plain,
% 1.41/1.37 (((~![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(s76, c_c2)) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | m_main_v_state2(s77, 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(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2)))),
% 1.41/1.37 inference(transitivity,[status(thm)],[6487, 6485])).
% 1.41/1.37 tff(6489,plain,
% 1.41/1.37 ((~![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(s76, c_c2)) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | m_main_v_state2(s77, c_n2))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6490,plain,
% 1.41/1.37 ((~![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(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~node14(s76, s77)) | (~m_main_v_state2(s76, c_c2))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6489, 6488])).
% 1.41/1.37 tff(6491,plain,
% 1.41/1.37 (m_main_v_state2(s77, c_n2) | node9(s76) | node8(s76) | node10(s76) | node11(s76) | node12(s76) | (~m_main_v_state2(s76, c_c2))),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6490, 726, 6484])).
% 1.41/1.37 tff(6492,plain,
% 1.41/1.37 (m_main_v_state2(s77, c_n2)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6491, 6473, 6428, 6465, 6461, 6453, 6436])).
% 1.41/1.37 tff(6493,plain,
% 1.41/1.37 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_c2)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6494,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_c2)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6495,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_c2))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6494, 6493])).
% 1.41/1.37 tff(6496,plain,
% 1.41/1.37 (~m_main_v_state2(s77, c_c2)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6495, 697, 6492])).
% 1.41/1.37 tff(6497,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s77, c_c2) | (~node3(s77)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s77, c_c2) | (~node3(s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6498,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s77, c_c2) | (~node3(s77)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6499,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s77, c_c2) | (~node3(s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6498, 6497])).
% 1.41/1.37 tff(6500,plain,
% 1.41/1.37 (~node3(s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6499, 399, 6496])).
% 1.41/1.37 tff(6501,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s76, c_n1) | (~node1(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s76, c_n1) | (~node1(s76)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6502,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s76, c_n1) | (~node1(s76)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6503,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s76, c_n1) | (~node1(s76))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6502, 6501])).
% 1.41/1.37 tff(6504,plain,
% 1.41/1.37 (~node1(s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6503, 421, 6449])).
% 1.41/1.37 tff(6505,plain,
% 1.41/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s75, s76)) | node18(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s75, s76)) | node18(s75, s76))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6506,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s75, s76)) | node18(s75, s76))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6507,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s75, s76)) | node18(s75, s76)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6506, 6505])).
% 1.41/1.37 tff(6508,plain,
% 1.41/1.37 (node18(s75, s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6507, 125, 6419])).
% 1.41/1.37 tff(6509,plain,
% 1.41/1.37 (((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, 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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, c_2))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6510,plain,
% 1.41/1.37 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, c_2))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6511,plain,
% 1.41/1.37 ((~![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(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | (~node18(s75, s76)) | m_main_v_turn(s76, c_2)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6510, 6509])).
% 1.41/1.37 tff(6512,plain,
% 1.41/1.37 ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state2(s75, c_t2)) | m_main_v_turn(s76, c_2)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6511, 760, 6508])).
% 1.41/1.37 tff(6513,plain,
% 1.41/1.37 (m_main_v_turn(s76, c_2)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6512, 6372, 6408])).
% 1.41/1.37 tff(6514,plain,
% 1.41/1.37 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s76, c_1)) | (~m_main_v_turn(s76, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s76, c_1)) | (~m_main_v_turn(s76, c_2)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6515,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s76, c_1)) | (~m_main_v_turn(s76, c_2)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6516,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s76, c_1)) | (~m_main_v_turn(s76, c_2))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6515, 6514])).
% 1.41/1.37 tff(6517,plain,
% 1.41/1.37 (~m_main_v_turn(s76, c_1)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6516, 156, 6513])).
% 1.41/1.37 tff(6518,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s76, c_1) | (~node5(s76)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s76, c_1) | (~node5(s76)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6519,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s76, c_1) | (~node5(s76)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6520,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s76, c_1) | (~node5(s76))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6519, 6518])).
% 1.41/1.37 tff(6521,plain,
% 1.41/1.37 (~node5(s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6520, 776, 6517])).
% 1.41/1.37 tff(6522,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s76, c_n1) | (~node2(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s76, c_n1) | (~node2(s76)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6523,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s76, c_n1) | (~node2(s76)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6524,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s76, c_n1) | (~node2(s76))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6523, 6522])).
% 1.41/1.37 tff(6525,plain,
% 1.41/1.37 (~node2(s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6524, 787, 6449])).
% 1.41/1.37 tff(6526,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s76, c_n1) | (~node3(s76)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s76, c_n1) | (~node3(s76)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6527,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s76, c_n1) | (~node3(s76)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6528,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s76, c_n1) | (~node3(s76))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6527, 6526])).
% 1.41/1.37 tff(6529,plain,
% 1.41/1.37 (~node3(s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6528, 798, 6449])).
% 1.41/1.37 tff(6530,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s76, c_n2) | (~node4(s76)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s76, c_n2) | (~node4(s76)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6531,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s76, c_n2) | (~node4(s76)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6532,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s76, c_n2) | (~node4(s76))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6531, 6530])).
% 1.41/1.37 tff(6533,plain,
% 1.41/1.37 (~node4(s76)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6532, 388, 6469])).
% 1.41/1.37 tff(6534,plain,
% 1.41/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s76, s77)) | node7(s76, s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s76, s77)) | node7(s76, s77))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6535,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s76, s77)) | node7(s76, s77))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6536,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s76, s77)) | node7(s76, s77)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6535, 6534])).
% 1.41/1.37 tff(6537,plain,
% 1.41/1.37 (node7(s76, s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6536, 206, 6480])).
% 1.41/1.37 tff(6538,plain,
% 1.41/1.37 (((~![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(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77)))) <=> ((~![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(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6539,plain,
% 1.41/1.37 ((~![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(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6540,plain,
% 1.41/1.37 ((~![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(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77) | (~node7(s76, s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6539, 6538])).
% 1.41/1.37 tff(6541,plain,
% 1.41/1.37 (m_main_v_state1(s76, c_c1) | node1(s76) | node2(s76) | node3(s76) | node4(s76) | node5(s76) | node6(s76, s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6540, 820, 6537])).
% 1.41/1.37 tff(6542,plain,
% 1.41/1.37 (node6(s76, s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6541, 6533, 6457, 6529, 6525, 6521, 6504])).
% 1.41/1.37 tff(6543,plain,
% 1.41/1.37 (((~![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(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77)))) <=> ((~![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(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6544,plain,
% 1.41/1.37 (((~node6(s76, s77)) | m_main_v_state1(s76, c_n1) | (~m_main_v_state1(s77, c_n1))) <=> (m_main_v_state1(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6545,plain,
% 1.41/1.37 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s76, s77)) | m_main_v_state1(s76, c_n1) | (~m_main_v_state1(s77, 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(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77))))),
% 1.41/1.37 inference(monotonicity,[status(thm)],[6544])).
% 1.41/1.37 tff(6546,plain,
% 1.41/1.37 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s76, s77)) | m_main_v_state1(s76, c_n1) | (~m_main_v_state1(s77, 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(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77)))),
% 1.41/1.37 inference(transitivity,[status(thm)],[6545, 6543])).
% 1.41/1.37 tff(6547,plain,
% 1.41/1.37 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s76, s77)) | m_main_v_state1(s76, c_n1) | (~m_main_v_state1(s77, c_n1)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6548,plain,
% 1.41/1.37 ((~![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(s76, c_n1) | (~m_main_v_state1(s77, c_n1)) | (~node6(s76, s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6547, 6546])).
% 1.41/1.37 tff(6549,plain,
% 1.41/1.37 (~m_main_v_state1(s77, c_n1)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6548, 835, 6449, 6542])).
% 1.41/1.37 tff(6550,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s77, c_n1) | (~node2(s77)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s77, c_n1) | (~node2(s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6551,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s77, c_n1) | (~node2(s77)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6552,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s77, c_n1) | (~node2(s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 1.41/1.37 tff(6553,plain,
% 1.41/1.37 (~node2(s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6552, 787, 6549])).
% 1.41/1.37 tff(6554,plain,
% 1.41/1.37 (((~![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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77)))) <=> ((~![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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6555,plain,
% 1.41/1.37 (((~node6(s76, s77)) | (~m_main_v_state1(s76, c_t1)) | m_main_v_state1(s77, c_t1)) <=> ((~m_main_v_state1(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6556,plain,
% 1.41/1.37 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s76, s77)) | (~m_main_v_state1(s76, c_t1)) | m_main_v_state1(s77, 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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77))))),
% 1.41/1.37 inference(monotonicity,[status(thm)],[6555])).
% 1.41/1.37 tff(6557,plain,
% 1.41/1.37 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s76, s77)) | (~m_main_v_state1(s76, c_t1)) | m_main_v_state1(s77, 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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77)))),
% 1.41/1.37 inference(transitivity,[status(thm)],[6556, 6554])).
% 1.41/1.37 tff(6558,plain,
% 1.41/1.37 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s76, s77)) | (~m_main_v_state1(s76, c_t1)) | m_main_v_state1(s77, c_t1))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6559,plain,
% 1.41/1.37 ((~![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(s76, c_t1)) | m_main_v_state1(s77, c_t1) | (~node6(s76, s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6558, 6557])).
% 1.41/1.37 tff(6560,plain,
% 1.41/1.37 (m_main_v_state1(s77, c_t1)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6559, 856, 6445, 6542])).
% 1.41/1.37 tff(6561,plain,
% 1.41/1.37 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_t2)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6562,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_t2)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6563,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s77, c_n2)) | (~m_main_v_state2(s77, c_t2))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6562, 6561])).
% 1.41/1.37 tff(6564,plain,
% 1.41/1.37 (~m_main_v_state2(s77, c_t2)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6563, 77, 6492])).
% 1.41/1.37 tff(6565,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s77, c_t2) | (~node1(s77)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s77, c_t2) | (~node1(s77)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6566,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s77, c_t2) | (~node1(s77)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6567,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s77, c_t2) | (~node1(s77))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 1.41/1.37 tff(6568,plain,
% 1.41/1.37 (~node1(s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6567, 195, 6564])).
% 1.41/1.37 tff(6569,plain,
% 1.41/1.37 (succ(s77, s78) <=> succ(s77, s78)),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6570,axiom,(succ(s77, s78)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound78')).
% 1.41/1.37 tff(6571,plain,
% 1.41/1.37 (succ(s77, s78)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6570, 6569])).
% 1.41/1.37 tff(6572,plain,
% 1.41/1.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6573,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6574,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6573, 6572])).
% 1.41/1.37 tff(6575,plain,
% 1.41/1.37 (trans(s77, s78)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6574, 6571, 39])).
% 1.41/1.37 tff(6576,plain,
% 1.41/1.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s77, s78)) | node7(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s77, s78)) | node7(s77, s78))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6577,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s77, s78)) | node7(s77, s78))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6578,plain,
% 1.41/1.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s77, s78)) | node7(s77, s78)),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6577, 6576])).
% 1.41/1.37 tff(6579,plain,
% 1.41/1.37 (node7(s77, s78)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6578, 206, 6575])).
% 1.41/1.37 tff(6580,plain,
% 1.41/1.37 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)))) <=> ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6581,plain,
% 1.41/1.37 (((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)) | m_main_v_state1(s78, c_c1)) <=> ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6582,plain,
% 1.41/1.37 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)) | m_main_v_state1(s78, 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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78))))),
% 1.41/1.37 inference(monotonicity,[status(thm)],[6581])).
% 1.41/1.37 tff(6583,plain,
% 1.41/1.37 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)) | m_main_v_state1(s78, 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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)))),
% 1.41/1.37 inference(transitivity,[status(thm)],[6582, 6580])).
% 1.41/1.37 tff(6584,plain,
% 1.41/1.37 ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78)) | m_main_v_state1(s78, c_c1))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6585,plain,
% 1.41/1.37 ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77) | (~node7(s77, s78))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6584, 6583])).
% 1.41/1.37 tff(6586,plain,
% 1.41/1.37 ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state1(s78, c_c1) | node1(s77) | node2(s77) | node3(s77)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6585, 892, 6579])).
% 1.41/1.37 tff(6587,plain,
% 1.41/1.37 (m_main_v_state1(s78, c_c1)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6586, 6568, 6492, 6560, 6553, 6500])).
% 1.41/1.37 tff(6588,plain,
% 1.41/1.37 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s78, c_t1)) | (~m_main_v_state1(s78, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s78, c_t1)) | (~m_main_v_state1(s78, c_c1)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6589,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s78, c_t1)) | (~m_main_v_state1(s78, c_c1)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6590,plain,
% 1.41/1.37 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s78, c_t1)) | (~m_main_v_state1(s78, c_c1))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6589, 6588])).
% 1.41/1.37 tff(6591,plain,
% 1.41/1.37 (~m_main_v_state1(s78, c_t1)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6590, 539, 6587])).
% 1.41/1.37 tff(6592,plain,
% 1.41/1.37 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s78, c_t1) | (~node5(s78)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s78, c_t1) | (~node5(s78)))),
% 1.41/1.37 inference(rewrite,[status(thm)],[])).
% 1.41/1.37 tff(6593,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s78, c_t1) | (~node5(s78)))),
% 1.41/1.37 inference(quant_inst,[status(thm)],[])).
% 1.41/1.37 tff(6594,plain,
% 1.41/1.37 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s78, c_t1) | (~node5(s78))),
% 1.41/1.37 inference(modus_ponens,[status(thm)],[6593, 6592])).
% 1.41/1.37 tff(6595,plain,
% 1.41/1.37 (~node5(s78)),
% 1.41/1.37 inference(unit_resolution,[status(thm)],[6594, 550, 6591])).
% 1.41/1.38 tff(6596,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s77, s78)) | node14(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s77, s78)) | node14(s77, s78))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6597,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s77, s78)) | node14(s77, s78))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6598,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s77, s78)) | node14(s77, s78)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6597, 6596])).
% 1.41/1.38 tff(6599,plain,
% 1.41/1.38 (node14(s77, s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6598, 7, 6575])).
% 1.41/1.38 tff(6600,plain,
% 1.41/1.38 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, 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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, c_t2))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6601,plain,
% 1.41/1.38 ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, c_t2))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6602,plain,
% 1.41/1.38 ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | (~node14(s77, s78)) | m_main_v_state2(s78, c_t2)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6601, 6600])).
% 1.41/1.38 tff(6603,plain,
% 1.41/1.38 ((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_state2(s78, c_t2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6602, 922, 6599])).
% 1.41/1.38 tff(6604,plain,
% 1.41/1.38 (m_main_v_state2(s78, c_t2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6603, 6560, 6492])).
% 1.41/1.38 tff(6605,plain,
% 1.41/1.38 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s78, c_n2)) | (~m_main_v_state2(s78, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s78, c_n2)) | (~m_main_v_state2(s78, c_t2)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6606,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s78, c_n2)) | (~m_main_v_state2(s78, c_t2)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6607,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s78, c_n2)) | (~m_main_v_state2(s78, c_t2))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6606, 6605])).
% 1.41/1.38 tff(6608,plain,
% 1.41/1.38 (~m_main_v_state2(s78, c_n2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6607, 77, 6604])).
% 1.41/1.38 tff(6609,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s78, c_n2) | (~node4(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s78, c_n2) | (~node4(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6610,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s78, c_n2) | (~node4(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6611,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s78, c_n2) | (~node4(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6610, 6609])).
% 1.41/1.38 tff(6612,plain,
% 1.41/1.38 (~node4(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6611, 388, 6608])).
% 1.41/1.38 tff(6613,plain,
% 1.41/1.38 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s78, c_t2)) | (~m_main_v_state2(s78, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s78, c_t2)) | (~m_main_v_state2(s78, c_c2)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6614,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s78, c_t2)) | (~m_main_v_state2(s78, c_c2)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6615,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s78, c_t2)) | (~m_main_v_state2(s78, c_c2))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6614, 6613])).
% 1.41/1.38 tff(6616,plain,
% 1.41/1.38 (~m_main_v_state2(s78, c_c2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6615, 260, 6604])).
% 1.41/1.38 tff(6617,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s78, c_c2) | (~node3(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s78, c_c2) | (~node3(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6618,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s78, c_c2) | (~node3(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6619,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s78, c_c2) | (~node3(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6618, 6617])).
% 1.41/1.38 tff(6620,plain,
% 1.41/1.38 (~node3(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6619, 399, 6616])).
% 1.41/1.38 tff(6621,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s78, c_n2) | (~node2(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s78, c_n2) | (~node2(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6622,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s78, c_n2) | (~node2(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6623,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s78, c_n2) | (~node2(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6622, 6621])).
% 1.41/1.38 tff(6624,plain,
% 1.41/1.38 (~node2(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6623, 410, 6608])).
% 1.41/1.38 tff(6625,plain,
% 1.41/1.38 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s78, c_n1)) | (~m_main_v_state1(s78, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s78, c_n1)) | (~m_main_v_state1(s78, c_c1)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6626,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s78, c_n1)) | (~m_main_v_state1(s78, c_c1)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6627,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s78, c_n1)) | (~m_main_v_state1(s78, c_c1))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6626, 6625])).
% 1.41/1.38 tff(6628,plain,
% 1.41/1.38 (~m_main_v_state1(s78, c_n1)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6627, 454, 6587])).
% 1.41/1.38 tff(6629,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s78, c_n1) | (~node1(s78)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s78, c_n1) | (~node1(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6630,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s78, c_n1) | (~node1(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6631,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s78, c_n1) | (~node1(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6630, 6629])).
% 1.41/1.38 tff(6632,plain,
% 1.41/1.38 (~node1(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6631, 421, 6628])).
% 1.41/1.38 tff(6633,plain,
% 1.41/1.38 (succ(s78, s79) <=> succ(s78, s79)),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6634,axiom,(succ(s78, s79)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound79')).
% 1.41/1.38 tff(6635,plain,
% 1.41/1.38 (succ(s78, s79)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6634, 6633])).
% 1.41/1.38 tff(6636,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6637,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6638,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6637, 6636])).
% 1.41/1.38 tff(6639,plain,
% 1.41/1.38 (trans(s78, s79)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6638, 6635, 39])).
% 1.41/1.38 tff(6640,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s78, s79)) | node7(s78, s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s78, s79)) | node7(s78, s79))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6641,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s78, s79)) | node7(s78, s79))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6642,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s78, s79)) | node7(s78, s79)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6641, 6640])).
% 1.41/1.38 tff(6643,plain,
% 1.41/1.38 (node7(s78, s79)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6642, 206, 6639])).
% 1.41/1.38 tff(6644,plain,
% 1.41/1.38 (((~![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(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)))) <=> ((~![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(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6645,plain,
% 1.41/1.38 (((~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)) | m_main_v_state1(s79, c_n1)) <=> (m_main_v_state1(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6646,plain,
% 1.41/1.38 (((~![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(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)) | m_main_v_state1(s79, 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(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79))))),
% 1.41/1.38 inference(monotonicity,[status(thm)],[6645])).
% 1.41/1.38 tff(6647,plain,
% 1.41/1.38 (((~![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(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)) | m_main_v_state1(s79, 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(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)))),
% 1.41/1.38 inference(transitivity,[status(thm)],[6646, 6644])).
% 1.41/1.38 tff(6648,plain,
% 1.41/1.38 ((~![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(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79)) | m_main_v_state1(s79, c_n1))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6649,plain,
% 1.41/1.38 ((~![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(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78) | (~node7(s78, s79))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6648, 6647])).
% 1.41/1.38 tff(6650,plain,
% 1.41/1.38 (m_main_v_state1(s79, c_n1) | (~m_main_v_state1(s78, c_c1)) | node1(s78) | node2(s78) | node3(s78) | node4(s78) | node5(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6649, 584, 6643])).
% 1.41/1.38 tff(6651,plain,
% 1.41/1.38 (m_main_v_state1(s79, c_n1)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6650, 6632, 6587, 6624, 6620, 6612, 6595])).
% 1.41/1.38 tff(6652,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s77, c_t2) | (~node15(s77)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s77, c_t2) | (~node15(s77)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6653,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s77, c_t2) | (~node15(s77)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6654,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s77, c_t2) | (~node15(s77))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6653, 6652])).
% 1.41/1.38 tff(6655,plain,
% 1.41/1.38 (~node15(s77)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6654, 103, 6564])).
% 1.41/1.38 tff(6656,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s77, s78)) | node18(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s77, s78)) | node18(s77, s78))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6657,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s77, s78)) | node18(s77, s78))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6658,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s77, s78)) | node18(s77, s78)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6657, 6656])).
% 1.41/1.38 tff(6659,plain,
% 1.41/1.38 (node18(s77, s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6658, 125, 6575])).
% 1.41/1.38 tff(6660,plain,
% 1.41/1.38 (((~![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(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, 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(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6661,plain,
% 1.41/1.38 (((~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node15(s77) | (~node18(s77, s78)) | m_main_v_turn(s78, c_1)) <=> (node15(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6662,plain,
% 1.41/1.38 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node15(s77) | (~node18(s77, s78)) | m_main_v_turn(s78, 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(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1)))),
% 1.41/1.38 inference(monotonicity,[status(thm)],[6661])).
% 1.41/1.38 tff(6663,plain,
% 1.41/1.38 (((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node15(s77) | (~node18(s77, s78)) | m_main_v_turn(s78, 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(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1))),
% 1.41/1.38 inference(transitivity,[status(thm)],[6662, 6660])).
% 1.41/1.38 tff(6664,plain,
% 1.41/1.38 ((~![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(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | node15(s77) | (~node18(s77, s78)) | m_main_v_turn(s78, c_1))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6665,plain,
% 1.41/1.38 ((~![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(s77) | (~node18(s77, s78)) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6664, 6663])).
% 1.41/1.38 tff(6666,plain,
% 1.41/1.38 (node15(s77) | (~m_main_v_state1(s77, c_t1)) | (~m_main_v_state2(s77, c_n2)) | m_main_v_turn(s78, c_1)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6665, 992, 6659])).
% 1.41/1.38 tff(6667,plain,
% 1.41/1.38 (m_main_v_turn(s78, c_1)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6666, 6655, 6492, 6560])).
% 1.41/1.38 tff(6668,plain,
% 1.41/1.38 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s78, c_1)) | (~m_main_v_turn(s78, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s78, c_1)) | (~m_main_v_turn(s78, c_2)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6669,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s78, c_1)) | (~m_main_v_turn(s78, c_2)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6670,plain,
% 1.41/1.38 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s78, c_1)) | (~m_main_v_turn(s78, c_2))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6669, 6668])).
% 1.41/1.38 tff(6671,plain,
% 1.41/1.38 (~m_main_v_turn(s78, c_2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6670, 156, 6667])).
% 1.41/1.38 tff(6672,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s78, c_2) | (~node12(s78)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s78, c_2) | (~node12(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6673,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s78, c_2) | (~node12(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6674,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s78, c_2) | (~node12(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6673, 6672])).
% 1.41/1.38 tff(6675,plain,
% 1.41/1.38 (~node12(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6674, 184, 6671])).
% 1.41/1.38 tff(6676,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s78, c_n2) | (~node8(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s78, c_n2) | (~node8(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6677,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s78, c_n2) | (~node8(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6678,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s78, c_n2) | (~node8(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6677, 6676])).
% 1.41/1.38 tff(6679,plain,
% 1.41/1.38 (~node8(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6678, 271, 6608])).
% 1.41/1.38 tff(6680,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s78, c_n2) | (~node9(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s78, c_n2) | (~node9(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6681,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s78, c_n2) | (~node9(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6682,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s78, c_n2) | (~node9(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 1.41/1.38 tff(6683,plain,
% 1.41/1.38 (~node9(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6682, 88, 6608])).
% 1.41/1.38 tff(6684,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s78, c_n2) | (~node10(s78)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s78, c_n2) | (~node10(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6685,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s78, c_n2) | (~node10(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6686,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s78, c_n2) | (~node10(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6685, 6684])).
% 1.41/1.38 tff(6687,plain,
% 1.41/1.38 (~node10(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6686, 249, 6608])).
% 1.41/1.38 tff(6688,plain,
% 1.41/1.38 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s78, c_n1) | (~node11(s78)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s78, c_n1) | (~node11(s78)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6689,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s78, c_n1) | (~node11(s78)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6690,plain,
% 1.41/1.38 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s78, c_n1) | (~node11(s78))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6689, 6688])).
% 1.41/1.38 tff(6691,plain,
% 1.41/1.38 (~node11(s78)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6690, 238, 6628])).
% 1.41/1.38 tff(6692,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s78, s79)) | node14(s78, s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s78, s79)) | node14(s78, s79))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6693,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s78, s79)) | node14(s78, s79))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6694,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s78, s79)) | node14(s78, s79)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6693, 6692])).
% 1.41/1.38 tff(6695,plain,
% 1.41/1.38 (node14(s78, s79)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6694, 7, 6639])).
% 1.41/1.38 tff(6696,plain,
% 1.41/1.38 (((~![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(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79) | (~node14(s78, s79)))) <=> ((~![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(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79) | (~node14(s78, s79)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6697,plain,
% 1.41/1.38 ((~![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(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79) | (~node14(s78, s79)))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6698,plain,
% 1.41/1.38 ((~![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(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79) | (~node14(s78, s79))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6697, 6696])).
% 1.41/1.38 tff(6699,plain,
% 1.41/1.38 (m_main_v_state2(s78, c_c2) | node9(s78) | node8(s78) | node10(s78) | node11(s78) | node12(s78) | node13(s78, s79)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6698, 296, 6695])).
% 1.41/1.38 tff(6700,plain,
% 1.41/1.38 (node13(s78, s79)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6699, 6691, 6616, 6687, 6683, 6679, 6675])).
% 1.41/1.38 tff(6701,plain,
% 1.41/1.38 (((~![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(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79)))) <=> ((~![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(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6702,plain,
% 1.41/1.38 (((~node13(s78, s79)) | (~m_main_v_state2(s78, c_t2)) | m_main_v_state2(s79, c_t2)) <=> ((~m_main_v_state2(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79)))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6703,plain,
% 1.41/1.38 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s78, s79)) | (~m_main_v_state2(s78, c_t2)) | m_main_v_state2(s79, 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(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79))))),
% 1.41/1.38 inference(monotonicity,[status(thm)],[6702])).
% 1.41/1.38 tff(6704,plain,
% 1.41/1.38 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s78, s79)) | (~m_main_v_state2(s78, c_t2)) | m_main_v_state2(s79, 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(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79)))),
% 1.41/1.38 inference(transitivity,[status(thm)],[6703, 6701])).
% 1.41/1.38 tff(6705,plain,
% 1.41/1.38 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s78, s79)) | (~m_main_v_state2(s78, c_t2)) | m_main_v_state2(s79, c_t2))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6706,plain,
% 1.41/1.38 ((~![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(s78, c_t2)) | m_main_v_state2(s79, c_t2) | (~node13(s78, s79))),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6705, 6704])).
% 1.41/1.38 tff(6707,plain,
% 1.41/1.38 (m_main_v_state2(s79, c_t2)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6706, 518, 6604, 6700])).
% 1.41/1.38 tff(6708,plain,
% 1.41/1.38 (succ(s79, s80) <=> succ(s79, s80)),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6709,axiom,(succ(s79, s80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound80')).
% 1.41/1.38 tff(6710,plain,
% 1.41/1.38 (succ(s79, s80)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6709, 6708])).
% 1.41/1.38 tff(6711,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6712,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6713,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6712, 6711])).
% 1.41/1.38 tff(6714,plain,
% 1.41/1.38 (trans(s79, s80)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6713, 6710, 39])).
% 1.41/1.38 tff(6715,plain,
% 1.41/1.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s79, s80)) | node7(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s79, s80)) | node7(s79, s80))),
% 1.41/1.38 inference(rewrite,[status(thm)],[])).
% 1.41/1.38 tff(6716,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s79, s80)) | node7(s79, s80))),
% 1.41/1.38 inference(quant_inst,[status(thm)],[])).
% 1.41/1.38 tff(6717,plain,
% 1.41/1.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s79, s80)) | node7(s79, s80)),
% 1.41/1.38 inference(modus_ponens,[status(thm)],[6716, 6715])).
% 1.41/1.38 tff(6718,plain,
% 1.41/1.38 (node7(s79, s80)),
% 1.41/1.38 inference(unit_resolution,[status(thm)],[6717, 206, 6714])).
% 1.41/1.38 tff(6719,plain,
% 1.41/1.38 (((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node7(s79, s80)) | m_main_v_state1(s80, 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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node7(s79, s80)) | m_main_v_state1(s80, c_t1))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6720,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node7(s79, s80)) | m_main_v_state1(s80, c_t1))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6721,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node7(s79, s80)) | m_main_v_state1(s80, c_t1)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6720, 6719])).
% 1.41/1.39 tff(6722,plain,
% 1.41/1.39 ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | m_main_v_state1(s80, c_t1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6721, 651, 6718])).
% 1.41/1.39 tff(6723,plain,
% 1.41/1.39 (m_main_v_state1(s80, c_t1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6722, 6707, 6651])).
% 1.41/1.39 tff(6724,plain,
% 1.41/1.39 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s80, c_n1)) | (~m_main_v_state1(s80, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s80, c_n1)) | (~m_main_v_state1(s80, c_t1)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6725,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s80, c_n1)) | (~m_main_v_state1(s80, c_t1)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6726,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s80, c_n1)) | (~m_main_v_state1(s80, c_t1))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6725, 6724])).
% 1.41/1.39 tff(6727,plain,
% 1.41/1.39 (~m_main_v_state1(s80, c_n1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6726, 17, 6723])).
% 1.41/1.39 tff(6728,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s80, c_n1) | (~node1(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s80, c_n1) | (~node1(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6729,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s80, c_n1) | (~node1(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6730,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s80, c_n1) | (~node1(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6729, 6728])).
% 1.41/1.39 tff(6731,plain,
% 1.41/1.39 (~node1(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6730, 421, 6727])).
% 1.41/1.39 tff(6732,plain,
% 1.41/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s79, s80)) | node18(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s79, s80)) | node18(s79, s80))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6733,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s79, s80)) | node18(s79, s80))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6734,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s79, s80)) | node18(s79, s80)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6733, 6732])).
% 1.41/1.39 tff(6735,plain,
% 1.41/1.39 (node18(s79, s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6734, 125, 6714])).
% 1.41/1.39 tff(6736,plain,
% 1.41/1.39 (((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, 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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, c_2))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6737,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, c_2))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6738,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | (~node18(s79, s80)) | m_main_v_turn(s80, c_2)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6737, 6736])).
% 1.41/1.39 tff(6739,plain,
% 1.41/1.39 ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | m_main_v_turn(s80, c_2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6738, 760, 6735])).
% 1.41/1.39 tff(6740,plain,
% 1.41/1.39 (m_main_v_turn(s80, c_2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6739, 6707, 6651])).
% 1.41/1.39 tff(6741,plain,
% 1.41/1.39 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s80, c_1)) | (~m_main_v_turn(s80, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s80, c_1)) | (~m_main_v_turn(s80, c_2)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6742,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s80, c_1)) | (~m_main_v_turn(s80, c_2)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6743,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s80, c_1)) | (~m_main_v_turn(s80, c_2))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6742, 6741])).
% 1.41/1.39 tff(6744,plain,
% 1.41/1.39 (~m_main_v_turn(s80, c_1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6743, 156, 6740])).
% 1.41/1.39 tff(6745,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s80, c_1) | (~node5(s80)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s80, c_1) | (~node5(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6746,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s80, c_1) | (~node5(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6747,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s80, c_1) | (~node5(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 1.41/1.39 tff(6748,plain,
% 1.41/1.39 (~node5(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6747, 776, 6744])).
% 1.41/1.39 tff(6749,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s80, c_n1) | (~node2(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s80, c_n1) | (~node2(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6750,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s80, c_n1) | (~node2(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6751,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s80, c_n1) | (~node2(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6750, 6749])).
% 1.41/1.39 tff(6752,plain,
% 1.41/1.39 (~node2(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6751, 787, 6727])).
% 1.41/1.39 tff(6753,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s80, c_n1) | (~node3(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s80, c_n1) | (~node3(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6754,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s80, c_n1) | (~node3(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6755,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s80, c_n1) | (~node3(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6754, 6753])).
% 1.41/1.39 tff(6756,plain,
% 1.41/1.39 (~node3(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6755, 798, 6727])).
% 1.41/1.39 tff(6757,plain,
% 1.41/1.39 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s80, c_t1)) | (~m_main_v_state1(s80, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s80, c_t1)) | (~m_main_v_state1(s80, c_c1)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6758,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s80, c_t1)) | (~m_main_v_state1(s80, c_c1)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6759,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s80, c_t1)) | (~m_main_v_state1(s80, c_c1))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6758, 6757])).
% 1.41/1.39 tff(6760,plain,
% 1.41/1.39 (~m_main_v_state1(s80, c_c1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6759, 539, 6723])).
% 1.41/1.39 tff(6761,plain,
% 1.41/1.39 (((~![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(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79)))) <=> ((~![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(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6762,plain,
% 1.41/1.39 (((~node13(s78, s79)) | m_main_v_state2(s78, c_n2) | (~m_main_v_state2(s79, c_n2))) <=> (m_main_v_state2(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6763,plain,
% 1.41/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s78, s79)) | m_main_v_state2(s78, c_n2) | (~m_main_v_state2(s79, 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(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79))))),
% 1.41/1.39 inference(monotonicity,[status(thm)],[6762])).
% 1.41/1.39 tff(6764,plain,
% 1.41/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s78, s79)) | m_main_v_state2(s78, c_n2) | (~m_main_v_state2(s79, 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(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79)))),
% 1.41/1.39 inference(transitivity,[status(thm)],[6763, 6761])).
% 1.41/1.39 tff(6765,plain,
% 1.41/1.39 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s78, s79)) | m_main_v_state2(s78, c_n2) | (~m_main_v_state2(s79, c_n2)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6766,plain,
% 1.41/1.39 ((~![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(s78, c_n2) | (~m_main_v_state2(s79, c_n2)) | (~node13(s78, s79))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6765, 6764])).
% 1.41/1.39 tff(6767,plain,
% 1.41/1.39 (~m_main_v_state2(s79, c_n2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6766, 311, 6608, 6700])).
% 1.41/1.39 tff(6768,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s79, c_n2) | (~node9(s79)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s79, c_n2) | (~node9(s79)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6769,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s79, c_n2) | (~node9(s79)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6770,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s79, c_n2) | (~node9(s79))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6769, 6768])).
% 1.41/1.39 tff(6771,plain,
% 1.41/1.39 (~node9(s79)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6770, 88, 6767])).
% 1.41/1.39 tff(6772,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s79, c_n2) | (~node10(s79)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s79, c_n2) | (~node10(s79)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6773,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s79, c_n2) | (~node10(s79)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6774,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s79, c_n2) | (~node10(s79))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6773, 6772])).
% 1.41/1.39 tff(6775,plain,
% 1.41/1.39 (~node10(s79)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6774, 249, 6767])).
% 1.41/1.39 tff(6776,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s79, c_n2) | (~node8(s79)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s79, c_n2) | (~node8(s79)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6777,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s79, c_n2) | (~node8(s79)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6778,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s79, c_n2) | (~node8(s79))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6777, 6776])).
% 1.41/1.39 tff(6779,plain,
% 1.41/1.39 (~node8(s79)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6778, 271, 6767])).
% 1.41/1.39 tff(6780,plain,
% 1.41/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s79, s80)) | node14(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s79, s80)) | node14(s79, s80))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6781,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s79, s80)) | node14(s79, s80))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6782,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s79, s80)) | node14(s79, s80)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6781, 6780])).
% 1.41/1.39 tff(6783,plain,
% 1.41/1.39 (node14(s79, s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6782, 7, 6714])).
% 1.41/1.39 tff(6784,plain,
% 1.41/1.39 (((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | node9(s79) | node8(s79) | node10(s79) | (~node14(s79, s80)) | m_main_v_state2(s80, 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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | node9(s79) | node8(s79) | node10(s79) | (~node14(s79, s80)) | m_main_v_state2(s80, c_c2))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6785,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | node9(s79) | node8(s79) | node10(s79) | (~node14(s79, s80)) | m_main_v_state2(s80, c_c2))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6786,plain,
% 1.41/1.39 ((~![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(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | node9(s79) | node8(s79) | node10(s79) | (~node14(s79, s80)) | m_main_v_state2(s80, c_c2)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6785, 6784])).
% 1.41/1.39 tff(6787,plain,
% 1.41/1.39 ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state2(s79, c_t2)) | node9(s79) | node8(s79) | node10(s79) | m_main_v_state2(s80, c_c2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6786, 617, 6783])).
% 1.41/1.39 tff(6788,plain,
% 1.41/1.39 (m_main_v_state2(s80, c_c2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6787, 6779, 6651, 6707, 6775, 6771])).
% 1.41/1.39 tff(6789,plain,
% 1.41/1.39 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s80, c_n2)) | (~m_main_v_state2(s80, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s80, c_n2)) | (~m_main_v_state2(s80, c_c2)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6790,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s80, c_n2)) | (~m_main_v_state2(s80, c_c2)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6791,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s80, c_n2)) | (~m_main_v_state2(s80, c_c2))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 1.41/1.39 tff(6792,plain,
% 1.41/1.39 (~m_main_v_state2(s80, c_n2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6791, 697, 6788])).
% 1.41/1.39 tff(6793,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s80, c_n2) | (~node4(s80)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s80, c_n2) | (~node4(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6794,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s80, c_n2) | (~node4(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6795,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s80, c_n2) | (~node4(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6794, 6793])).
% 1.41/1.39 tff(6796,plain,
% 1.41/1.39 (~node4(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6795, 388, 6792])).
% 1.41/1.39 tff(6797,plain,
% 1.41/1.39 (succ(s80, s81) <=> succ(s80, s81)),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6798,axiom,(succ(s80, s81)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound81')).
% 1.41/1.39 tff(6799,plain,
% 1.41/1.39 (succ(s80, s81)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 1.41/1.39 tff(6800,plain,
% 1.41/1.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6801,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6802,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6801, 6800])).
% 1.41/1.39 tff(6803,plain,
% 1.41/1.39 (trans(s80, s81)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6802, 6799, 39])).
% 1.41/1.39 tff(6804,plain,
% 1.41/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s80, s81)) | node7(s80, s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s80, s81)) | node7(s80, s81))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6805,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s80, s81)) | node7(s80, s81))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6806,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s80, s81)) | node7(s80, s81)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6805, 6804])).
% 1.41/1.39 tff(6807,plain,
% 1.41/1.39 (node7(s80, s81)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6806, 206, 6803])).
% 1.41/1.39 tff(6808,plain,
% 1.41/1.39 (((~![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(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81) | (~node7(s80, s81)))) <=> ((~![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(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81) | (~node7(s80, s81)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6809,plain,
% 1.41/1.39 ((~![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(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81) | (~node7(s80, s81)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6810,plain,
% 1.41/1.39 ((~![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(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81) | (~node7(s80, s81))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6809, 6808])).
% 1.41/1.39 tff(6811,plain,
% 1.41/1.39 (m_main_v_state1(s80, c_c1) | node1(s80) | node2(s80) | node3(s80) | node4(s80) | node5(s80) | node6(s80, s81)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6810, 820, 6807])).
% 1.41/1.39 tff(6812,plain,
% 1.41/1.39 (node6(s80, s81)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6811, 6796, 6760, 6756, 6752, 6748, 6731])).
% 1.41/1.39 tff(6813,plain,
% 1.41/1.39 (((~![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(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81)))) <=> ((~![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(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6814,plain,
% 1.41/1.39 (((~node6(s80, s81)) | (~m_main_v_state1(s80, c_t1)) | m_main_v_state1(s81, c_t1)) <=> ((~m_main_v_state1(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6815,plain,
% 1.41/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s80, s81)) | (~m_main_v_state1(s80, c_t1)) | m_main_v_state1(s81, 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(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81))))),
% 1.41/1.39 inference(monotonicity,[status(thm)],[6814])).
% 1.41/1.39 tff(6816,plain,
% 1.41/1.39 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s80, s81)) | (~m_main_v_state1(s80, c_t1)) | m_main_v_state1(s81, 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(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81)))),
% 1.41/1.39 inference(transitivity,[status(thm)],[6815, 6813])).
% 1.41/1.39 tff(6817,plain,
% 1.41/1.39 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s80, s81)) | (~m_main_v_state1(s80, c_t1)) | m_main_v_state1(s81, c_t1))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6818,plain,
% 1.41/1.39 ((~![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(s80, c_t1)) | m_main_v_state1(s81, c_t1) | (~node6(s80, s81))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6817, 6816])).
% 1.41/1.39 tff(6819,plain,
% 1.41/1.39 (m_main_v_state1(s81, c_t1)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6818, 856, 6723, 6812])).
% 1.41/1.39 tff(6820,plain,
% 1.41/1.39 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s80, c_t2)) | (~m_main_v_state2(s80, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s80, c_t2)) | (~m_main_v_state2(s80, c_c2)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6821,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s80, c_t2)) | (~m_main_v_state2(s80, c_c2)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6822,plain,
% 1.41/1.39 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s80, c_t2)) | (~m_main_v_state2(s80, c_c2))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6821, 6820])).
% 1.41/1.39 tff(6823,plain,
% 1.41/1.39 (~m_main_v_state2(s80, c_t2)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6822, 260, 6788])).
% 1.41/1.39 tff(6824,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s80, c_t2) | (~node12(s80)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s80, c_t2) | (~node12(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6825,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s80, c_t2) | (~node12(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6826,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s80, c_t2) | (~node12(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6825, 6824])).
% 1.41/1.39 tff(6827,plain,
% 1.41/1.39 (~node12(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6826, 633, 6823])).
% 1.41/1.39 tff(6828,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s80, c_n1) | (~node11(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s80, c_n1) | (~node11(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6829,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s80, c_n1) | (~node11(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6830,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s80, c_n1) | (~node11(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6829, 6828])).
% 1.41/1.39 tff(6831,plain,
% 1.41/1.39 (~node11(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6830, 238, 6727])).
% 1.41/1.39 tff(6832,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s80, c_c1) | (~node10(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s80, c_c1) | (~node10(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6833,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s80, c_c1) | (~node10(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6834,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s80, c_c1) | (~node10(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6833, 6832])).
% 1.41/1.39 tff(6835,plain,
% 1.41/1.39 (~node10(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6834, 675, 6760])).
% 1.41/1.39 tff(6836,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s80, c_n1) | (~node9(s80)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s80, c_n1) | (~node9(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6837,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s80, c_n1) | (~node9(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6838,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s80, c_n1) | (~node9(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6837, 6836])).
% 1.41/1.39 tff(6839,plain,
% 1.41/1.39 (~node9(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6838, 686, 6727])).
% 1.41/1.39 tff(6840,plain,
% 1.41/1.39 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s80, c_n2) | (~node8(s80)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s80, c_n2) | (~node8(s80)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6841,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s80, c_n2) | (~node8(s80)))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6842,plain,
% 1.41/1.39 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s80, c_n2) | (~node8(s80))),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6841, 6840])).
% 1.41/1.39 tff(6843,plain,
% 1.41/1.39 (~node8(s80)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6842, 271, 6792])).
% 1.41/1.39 tff(6844,plain,
% 1.41/1.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s80, s81)) | node14(s80, s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s80, s81)) | node14(s80, s81))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6845,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s80, s81)) | node14(s80, s81))),
% 1.41/1.39 inference(quant_inst,[status(thm)],[])).
% 1.41/1.39 tff(6846,plain,
% 1.41/1.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s80, s81)) | node14(s80, s81)),
% 1.41/1.39 inference(modus_ponens,[status(thm)],[6845, 6844])).
% 1.41/1.39 tff(6847,plain,
% 1.41/1.39 (node14(s80, s81)),
% 1.41/1.39 inference(unit_resolution,[status(thm)],[6846, 7, 6803])).
% 1.41/1.39 tff(6848,plain,
% 1.41/1.39 (((~![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(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, 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(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, c_c2)))),
% 1.41/1.39 inference(rewrite,[status(thm)],[])).
% 1.41/1.39 tff(6849,plain,
% 1.41/1.39 (((~m_main_v_state2(s80, c_c2)) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | m_main_v_state2(s81, c_n2)) <=> (m_main_v_state2(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, c_c2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6850,plain,
% 1.48/1.40 (((~![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(s80, c_c2)) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | m_main_v_state2(s81, 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(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, c_c2))))),
% 1.48/1.40 inference(monotonicity,[status(thm)],[6849])).
% 1.48/1.40 tff(6851,plain,
% 1.48/1.40 (((~![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(s80, c_c2)) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | m_main_v_state2(s81, 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(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, c_c2)))),
% 1.48/1.40 inference(transitivity,[status(thm)],[6850, 6848])).
% 1.48/1.40 tff(6852,plain,
% 1.48/1.40 ((~![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(s80, c_c2)) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | m_main_v_state2(s81, c_n2))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6853,plain,
% 1.48/1.40 ((~![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(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~node14(s80, s81)) | (~m_main_v_state2(s80, c_c2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6852, 6851])).
% 1.48/1.40 tff(6854,plain,
% 1.48/1.40 (m_main_v_state2(s81, c_n2) | node9(s80) | node8(s80) | node10(s80) | node11(s80) | node12(s80) | (~m_main_v_state2(s80, c_c2))),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6853, 726, 6847])).
% 1.48/1.40 tff(6855,plain,
% 1.48/1.40 (m_main_v_state2(s81, c_n2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6854, 6843, 6788, 6839, 6835, 6831, 6827])).
% 1.48/1.40 tff(6856,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_t2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6857,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_t2)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6858,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_t2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6857, 6856])).
% 1.48/1.40 tff(6859,plain,
% 1.48/1.40 (~m_main_v_state2(s81, c_t2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6858, 77, 6855])).
% 1.48/1.40 tff(6860,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s81, c_t2) | (~node15(s81)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s81, c_t2) | (~node15(s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6861,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s81, c_t2) | (~node15(s81)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6862,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s81, c_t2) | (~node15(s81))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6861, 6860])).
% 1.48/1.40 tff(6863,plain,
% 1.48/1.40 (~node15(s81)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6862, 103, 6859])).
% 1.48/1.40 tff(6864,plain,
% 1.48/1.40 (succ(s81, s82) <=> succ(s81, s82)),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6865,axiom,(succ(s81, s82)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound82')).
% 1.48/1.40 tff(6866,plain,
% 1.48/1.40 (succ(s81, s82)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6865, 6864])).
% 1.48/1.40 tff(6867,plain,
% 1.48/1.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6868,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6869,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6868, 6867])).
% 1.48/1.40 tff(6870,plain,
% 1.48/1.40 (trans(s81, s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6869, 6866, 39])).
% 1.48/1.40 tff(6871,plain,
% 1.48/1.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s81, s82)) | node18(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s81, s82)) | node18(s81, s82))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6872,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s81, s82)) | node18(s81, s82))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6873,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s81, s82)) | node18(s81, s82)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6872, 6871])).
% 1.48/1.40 tff(6874,plain,
% 1.48/1.40 (node18(s81, s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6873, 125, 6870])).
% 1.48/1.40 tff(6875,plain,
% 1.48/1.40 (((~![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(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, 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(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6876,plain,
% 1.48/1.40 (((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node15(s81) | (~node18(s81, s82)) | m_main_v_turn(s82, c_1)) <=> (node15(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6877,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node15(s81) | (~node18(s81, s82)) | m_main_v_turn(s82, 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(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1)))),
% 1.48/1.40 inference(monotonicity,[status(thm)],[6876])).
% 1.48/1.40 tff(6878,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node15(s81) | (~node18(s81, s82)) | m_main_v_turn(s82, 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(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1))),
% 1.48/1.40 inference(transitivity,[status(thm)],[6877, 6875])).
% 1.48/1.40 tff(6879,plain,
% 1.48/1.40 ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node15(s81) | (~node18(s81, s82)) | m_main_v_turn(s82, c_1))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6880,plain,
% 1.48/1.40 ((~![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(s81) | (~node18(s81, s82)) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6879, 6878])).
% 1.48/1.40 tff(6881,plain,
% 1.48/1.40 (node15(s81) | (~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_turn(s82, c_1)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6880, 992, 6874])).
% 1.48/1.40 tff(6882,plain,
% 1.48/1.40 (m_main_v_turn(s82, c_1)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6881, 6863, 6855, 6819])).
% 1.48/1.40 tff(6883,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s82, c_1)) | (~m_main_v_turn(s82, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s82, c_1)) | (~m_main_v_turn(s82, c_2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6884,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s82, c_1)) | (~m_main_v_turn(s82, c_2)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6885,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s82, c_1)) | (~m_main_v_turn(s82, c_2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6884, 6883])).
% 1.48/1.40 tff(6886,plain,
% 1.48/1.40 (~m_main_v_turn(s82, c_2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6885, 156, 6882])).
% 1.48/1.40 tff(6887,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s82, c_2) | (~node12(s82)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s82, c_2) | (~node12(s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6888,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s82, c_2) | (~node12(s82)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6889,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s82, c_2) | (~node12(s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6888, 6887])).
% 1.48/1.40 tff(6890,plain,
% 1.48/1.40 (~node12(s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6889, 184, 6886])).
% 1.48/1.40 tff(6891,plain,
% 1.48/1.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s81, s82)) | node14(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s81, s82)) | node14(s81, s82))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6892,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s81, s82)) | node14(s81, s82))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6893,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s81, s82)) | node14(s81, s82)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 1.48/1.40 tff(6894,plain,
% 1.48/1.40 (node14(s81, s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6893, 7, 6870])).
% 1.48/1.40 tff(6895,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | (~node14(s81, s82)) | m_main_v_state2(s82, 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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | (~node14(s81, s82)) | m_main_v_state2(s82, c_t2))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6896,plain,
% 1.48/1.40 ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | (~node14(s81, s82)) | m_main_v_state2(s82, c_t2))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6897,plain,
% 1.48/1.40 ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | (~node14(s81, s82)) | m_main_v_state2(s82, c_t2)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6896, 6895])).
% 1.48/1.40 tff(6898,plain,
% 1.48/1.40 ((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state2(s82, c_t2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6897, 922, 6894])).
% 1.48/1.40 tff(6899,plain,
% 1.48/1.40 (m_main_v_state2(s82, c_t2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6898, 6819, 6855])).
% 1.48/1.40 tff(6900,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s82, c_n2)) | (~m_main_v_state2(s82, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s82, c_n2)) | (~m_main_v_state2(s82, c_t2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6901,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s82, c_n2)) | (~m_main_v_state2(s82, c_t2)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6902,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s82, c_n2)) | (~m_main_v_state2(s82, c_t2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6901, 6900])).
% 1.48/1.40 tff(6903,plain,
% 1.48/1.40 (~m_main_v_state2(s82, c_n2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6902, 77, 6899])).
% 1.48/1.40 tff(6904,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s82, c_n2) | (~node8(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s82, c_n2) | (~node8(s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6905,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s82, c_n2) | (~node8(s82)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6906,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s82, c_n2) | (~node8(s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6905, 6904])).
% 1.48/1.40 tff(6907,plain,
% 1.48/1.40 (~node8(s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6906, 271, 6903])).
% 1.48/1.40 tff(6908,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s82, c_n2) | (~node9(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s82, c_n2) | (~node9(s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6909,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s82, c_n2) | (~node9(s82)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6910,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s82, c_n2) | (~node9(s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 1.48/1.40 tff(6911,plain,
% 1.48/1.40 (~node9(s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6910, 88, 6903])).
% 1.48/1.40 tff(6912,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s82, c_n2) | (~node10(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s82, c_n2) | (~node10(s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6913,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s82, c_n2) | (~node10(s82)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6914,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s82, c_n2) | (~node10(s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6913, 6912])).
% 1.48/1.40 tff(6915,plain,
% 1.48/1.40 (~node10(s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6914, 249, 6903])).
% 1.48/1.40 tff(6916,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s82, c_t2)) | (~m_main_v_state2(s82, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s82, c_t2)) | (~m_main_v_state2(s82, c_c2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6917,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s82, c_t2)) | (~m_main_v_state2(s82, c_c2)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6918,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s82, c_t2)) | (~m_main_v_state2(s82, c_c2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6917, 6916])).
% 1.48/1.40 tff(6919,plain,
% 1.48/1.40 (~m_main_v_state2(s82, c_c2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6918, 260, 6899])).
% 1.48/1.40 tff(6920,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_c2)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6921,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_c2)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6922,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s81, c_n2)) | (~m_main_v_state2(s81, c_c2))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.48/1.40 tff(6923,plain,
% 1.48/1.40 (~m_main_v_state2(s81, c_c2)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6922, 697, 6855])).
% 1.48/1.40 tff(6924,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s81, c_c2) | (~node3(s81)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s81, c_c2) | (~node3(s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6925,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s81, c_c2) | (~node3(s81)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6926,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s81, c_c2) | (~node3(s81))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6925, 6924])).
% 1.48/1.40 tff(6927,plain,
% 1.48/1.40 (~node3(s81)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6926, 399, 6923])).
% 1.48/1.40 tff(6928,plain,
% 1.48/1.40 (((~![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(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81)))) <=> ((~![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(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6929,plain,
% 1.48/1.40 (((~node6(s80, s81)) | m_main_v_state1(s80, c_n1) | (~m_main_v_state1(s81, c_n1))) <=> (m_main_v_state1(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6930,plain,
% 1.48/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s80, s81)) | m_main_v_state1(s80, c_n1) | (~m_main_v_state1(s81, 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(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81))))),
% 1.48/1.40 inference(monotonicity,[status(thm)],[6929])).
% 1.48/1.40 tff(6931,plain,
% 1.48/1.40 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s80, s81)) | m_main_v_state1(s80, c_n1) | (~m_main_v_state1(s81, 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(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81)))),
% 1.48/1.40 inference(transitivity,[status(thm)],[6930, 6928])).
% 1.48/1.40 tff(6932,plain,
% 1.48/1.40 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s80, s81)) | m_main_v_state1(s80, c_n1) | (~m_main_v_state1(s81, c_n1)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6933,plain,
% 1.48/1.40 ((~![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(s80, c_n1) | (~m_main_v_state1(s81, c_n1)) | (~node6(s80, s81))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 1.48/1.40 tff(6934,plain,
% 1.48/1.40 (~m_main_v_state1(s81, c_n1)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6933, 835, 6727, 6812])).
% 1.48/1.40 tff(6935,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s81, c_n1) | (~node2(s81)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s81, c_n1) | (~node2(s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6936,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s81, c_n1) | (~node2(s81)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6937,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s81, c_n1) | (~node2(s81))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6936, 6935])).
% 1.48/1.40 tff(6938,plain,
% 1.48/1.40 (~node2(s81)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6937, 787, 6934])).
% 1.48/1.40 tff(6939,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s81, c_t2) | (~node1(s81)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s81, c_t2) | (~node1(s81)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6940,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s81, c_t2) | (~node1(s81)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6941,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s81, c_t2) | (~node1(s81))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 1.48/1.40 tff(6942,plain,
% 1.48/1.40 (~node1(s81)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6941, 195, 6859])).
% 1.48/1.40 tff(6943,plain,
% 1.48/1.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s81, s82)) | node7(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s81, s82)) | node7(s81, s82))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6944,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s81, s82)) | node7(s81, s82))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6945,plain,
% 1.48/1.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s81, s82)) | node7(s81, s82)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 1.48/1.40 tff(6946,plain,
% 1.48/1.40 (node7(s81, s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6945, 206, 6870])).
% 1.48/1.40 tff(6947,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)))) <=> ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6948,plain,
% 1.48/1.40 (((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)) | m_main_v_state1(s82, c_c1)) <=> ((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6949,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)) | m_main_v_state1(s82, 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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82))))),
% 1.48/1.40 inference(monotonicity,[status(thm)],[6948])).
% 1.48/1.40 tff(6950,plain,
% 1.48/1.40 (((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)) | m_main_v_state1(s82, 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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)))),
% 1.48/1.40 inference(transitivity,[status(thm)],[6949, 6947])).
% 1.48/1.40 tff(6951,plain,
% 1.48/1.40 ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82)) | m_main_v_state1(s82, c_c1))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6952,plain,
% 1.48/1.40 ((~![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(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81) | (~node7(s81, s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6951, 6950])).
% 1.48/1.40 tff(6953,plain,
% 1.48/1.40 ((~m_main_v_state1(s81, c_t1)) | (~m_main_v_state2(s81, c_n2)) | m_main_v_state1(s82, c_c1) | node1(s81) | node2(s81) | node3(s81)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6952, 892, 6946])).
% 1.48/1.40 tff(6954,plain,
% 1.48/1.40 (m_main_v_state1(s82, c_c1)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6953, 6942, 6855, 6819, 6938, 6927])).
% 1.48/1.40 tff(6955,plain,
% 1.48/1.40 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s82, c_n1)) | (~m_main_v_state1(s82, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s82, c_n1)) | (~m_main_v_state1(s82, c_c1)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6956,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s82, c_n1)) | (~m_main_v_state1(s82, c_c1)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6957,plain,
% 1.48/1.40 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s82, c_n1)) | (~m_main_v_state1(s82, c_c1))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 1.48/1.40 tff(6958,plain,
% 1.48/1.40 (~m_main_v_state1(s82, c_n1)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6957, 454, 6954])).
% 1.48/1.40 tff(6959,plain,
% 1.48/1.40 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s82, c_n1) | (~node11(s82)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s82, c_n1) | (~node11(s82)))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6960,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s82, c_n1) | (~node11(s82)))),
% 1.48/1.40 inference(quant_inst,[status(thm)],[])).
% 1.48/1.40 tff(6961,plain,
% 1.48/1.40 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s82, c_n1) | (~node11(s82))),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6960, 6959])).
% 1.48/1.40 tff(6962,plain,
% 1.48/1.40 (~node11(s82)),
% 1.48/1.40 inference(unit_resolution,[status(thm)],[6961, 238, 6958])).
% 1.48/1.40 tff(6963,plain,
% 1.48/1.40 (succ(s82, s83) <=> succ(s82, s83)),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.40 tff(6964,axiom,(succ(s82, s83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound83')).
% 1.48/1.40 tff(6965,plain,
% 1.48/1.40 (succ(s82, s83)),
% 1.48/1.40 inference(modus_ponens,[status(thm)],[6964, 6963])).
% 1.48/1.40 tff(6966,plain,
% 1.48/1.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83))),
% 1.48/1.40 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6967,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6968,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6967, 6966])).
% 1.48/1.41 tff(6969,plain,
% 1.48/1.41 (trans(s82, s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6968, 6965, 39])).
% 1.48/1.41 tff(6970,plain,
% 1.48/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s82, s83)) | node14(s82, s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s82, s83)) | node14(s82, s83))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6971,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s82, s83)) | node14(s82, s83))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6972,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s82, s83)) | node14(s82, s83)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6971, 6970])).
% 1.48/1.41 tff(6973,plain,
% 1.48/1.41 (node14(s82, s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6972, 7, 6969])).
% 1.48/1.41 tff(6974,plain,
% 1.48/1.41 (((~![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(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83) | (~node14(s82, s83)))) <=> ((~![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(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83) | (~node14(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6975,plain,
% 1.48/1.41 ((~![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(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83) | (~node14(s82, s83)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6976,plain,
% 1.48/1.41 ((~![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(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83) | (~node14(s82, s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 1.48/1.41 tff(6977,plain,
% 1.48/1.41 (m_main_v_state2(s82, c_c2) | node9(s82) | node8(s82) | node10(s82) | node11(s82) | node12(s82) | node13(s82, s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6976, 296, 6973])).
% 1.48/1.41 tff(6978,plain,
% 1.48/1.41 (node13(s82, s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6977, 6962, 6919, 6915, 6911, 6907, 6890])).
% 1.48/1.41 tff(6979,plain,
% 1.48/1.41 (((~![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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83)))) <=> ((~![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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6980,plain,
% 1.48/1.41 (((~node13(s82, s83)) | m_main_v_state2(s82, c_n2) | (~m_main_v_state2(s83, c_n2))) <=> (m_main_v_state2(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6981,plain,
% 1.48/1.41 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s82, s83)) | m_main_v_state2(s82, c_n2) | (~m_main_v_state2(s83, 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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83))))),
% 1.48/1.41 inference(monotonicity,[status(thm)],[6980])).
% 1.48/1.41 tff(6982,plain,
% 1.48/1.41 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s82, s83)) | m_main_v_state2(s82, c_n2) | (~m_main_v_state2(s83, 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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83)))),
% 1.48/1.41 inference(transitivity,[status(thm)],[6981, 6979])).
% 1.48/1.41 tff(6983,plain,
% 1.48/1.41 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s82, s83)) | m_main_v_state2(s82, c_n2) | (~m_main_v_state2(s83, c_n2)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6984,plain,
% 1.48/1.41 ((~![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(s82, c_n2) | (~m_main_v_state2(s83, c_n2)) | (~node13(s82, s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6983, 6982])).
% 1.48/1.41 tff(6985,plain,
% 1.48/1.41 (~m_main_v_state2(s83, c_n2)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6984, 311, 6903, 6978])).
% 1.48/1.41 tff(6986,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s83, c_n2) | (~node9(s83)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s83, c_n2) | (~node9(s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6987,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s83, c_n2) | (~node9(s83)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6988,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s83, c_n2) | (~node9(s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6987, 6986])).
% 1.48/1.41 tff(6989,plain,
% 1.48/1.41 (~node9(s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6988, 88, 6985])).
% 1.48/1.41 tff(6990,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s83, c_n2) | (~node10(s83)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s83, c_n2) | (~node10(s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6991,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s83, c_n2) | (~node10(s83)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6992,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s83, c_n2) | (~node10(s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6991, 6990])).
% 1.48/1.41 tff(6993,plain,
% 1.48/1.41 (~node10(s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6992, 249, 6985])).
% 1.48/1.41 tff(6994,plain,
% 1.48/1.41 (((~![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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83)))) <=> ((~![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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6995,plain,
% 1.48/1.41 (((~node13(s82, s83)) | (~m_main_v_state2(s82, c_t2)) | m_main_v_state2(s83, c_t2)) <=> ((~m_main_v_state2(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(6996,plain,
% 1.48/1.41 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s82, s83)) | (~m_main_v_state2(s82, c_t2)) | m_main_v_state2(s83, 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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83))))),
% 1.48/1.41 inference(monotonicity,[status(thm)],[6995])).
% 1.48/1.41 tff(6997,plain,
% 1.48/1.41 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s82, s83)) | (~m_main_v_state2(s82, c_t2)) | m_main_v_state2(s83, 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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83)))),
% 1.48/1.41 inference(transitivity,[status(thm)],[6996, 6994])).
% 1.48/1.41 tff(6998,plain,
% 1.48/1.41 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s82, s83)) | (~m_main_v_state2(s82, c_t2)) | m_main_v_state2(s83, c_t2))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(6999,plain,
% 1.48/1.41 ((~![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(s82, c_t2)) | m_main_v_state2(s83, c_t2) | (~node13(s82, s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[6998, 6997])).
% 1.48/1.41 tff(7000,plain,
% 1.48/1.41 (m_main_v_state2(s83, c_t2)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[6999, 518, 6899, 6978])).
% 1.48/1.41 tff(7001,plain,
% 1.48/1.41 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s82, c_t1)) | (~m_main_v_state1(s82, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s82, c_t1)) | (~m_main_v_state1(s82, c_c1)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7002,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s82, c_t1)) | (~m_main_v_state1(s82, c_c1)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7003,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s82, c_t1)) | (~m_main_v_state1(s82, c_c1))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7002, 7001])).
% 1.48/1.41 tff(7004,plain,
% 1.48/1.41 (~m_main_v_state1(s82, c_t1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7003, 539, 6954])).
% 1.48/1.41 tff(7005,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s82, c_t1) | (~node5(s82)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s82, c_t1) | (~node5(s82)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7006,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s82, c_t1) | (~node5(s82)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7007,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s82, c_t1) | (~node5(s82))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7006, 7005])).
% 1.48/1.41 tff(7008,plain,
% 1.48/1.41 (~node5(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7007, 550, 7004])).
% 1.48/1.41 tff(7009,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s82, c_n2) | (~node4(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s82, c_n2) | (~node4(s82)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7010,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s82, c_n2) | (~node4(s82)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7011,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s82, c_n2) | (~node4(s82))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7010, 7009])).
% 1.48/1.41 tff(7012,plain,
% 1.48/1.41 (~node4(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7011, 388, 6903])).
% 1.48/1.41 tff(7013,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s82, c_c2) | (~node3(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s82, c_c2) | (~node3(s82)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7014,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s82, c_c2) | (~node3(s82)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7015,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s82, c_c2) | (~node3(s82))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 1.48/1.41 tff(7016,plain,
% 1.48/1.41 (~node3(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7015, 399, 6919])).
% 1.48/1.41 tff(7017,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s82, c_n2) | (~node2(s82)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s82, c_n2) | (~node2(s82)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7018,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s82, c_n2) | (~node2(s82)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7019,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s82, c_n2) | (~node2(s82))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 1.48/1.41 tff(7020,plain,
% 1.48/1.41 (~node2(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7019, 410, 6903])).
% 1.48/1.41 tff(7021,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s82, c_n1) | (~node1(s82)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s82, c_n1) | (~node1(s82)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7022,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s82, c_n1) | (~node1(s82)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7023,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s82, c_n1) | (~node1(s82))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7022, 7021])).
% 1.48/1.41 tff(7024,plain,
% 1.48/1.41 (~node1(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7023, 421, 6958])).
% 1.48/1.41 tff(7025,plain,
% 1.48/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s82, s83)) | node7(s82, s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s82, s83)) | node7(s82, s83))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7026,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s82, s83)) | node7(s82, s83))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7027,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s82, s83)) | node7(s82, s83)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7026, 7025])).
% 1.48/1.41 tff(7028,plain,
% 1.48/1.41 (node7(s82, s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7027, 206, 6969])).
% 1.48/1.41 tff(7029,plain,
% 1.48/1.41 (((~![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(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)))) <=> ((~![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(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7030,plain,
% 1.48/1.41 (((~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)) | m_main_v_state1(s83, c_n1)) <=> (m_main_v_state1(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7031,plain,
% 1.48/1.41 (((~![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(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)) | m_main_v_state1(s83, 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(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83))))),
% 1.48/1.41 inference(monotonicity,[status(thm)],[7030])).
% 1.48/1.41 tff(7032,plain,
% 1.48/1.41 (((~![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(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)) | m_main_v_state1(s83, 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(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)))),
% 1.48/1.41 inference(transitivity,[status(thm)],[7031, 7029])).
% 1.48/1.41 tff(7033,plain,
% 1.48/1.41 ((~![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(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83)) | m_main_v_state1(s83, c_n1))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7034,plain,
% 1.48/1.41 ((~![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(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82) | (~node7(s82, s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7033, 7032])).
% 1.48/1.41 tff(7035,plain,
% 1.48/1.41 (m_main_v_state1(s83, c_n1) | (~m_main_v_state1(s82, c_c1)) | node1(s82) | node2(s82) | node3(s82) | node4(s82) | node5(s82)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7034, 584, 7028])).
% 1.48/1.41 tff(7036,plain,
% 1.48/1.41 (m_main_v_state1(s83, c_n1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7035, 7024, 6954, 7020, 7016, 7012, 7008])).
% 1.48/1.41 tff(7037,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s83, c_n2) | (~node8(s83)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s83, c_n2) | (~node8(s83)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7038,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s83, c_n2) | (~node8(s83)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7039,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s83, c_n2) | (~node8(s83))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7038, 7037])).
% 1.48/1.41 tff(7040,plain,
% 1.48/1.41 (~node8(s83)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7039, 271, 6985])).
% 1.48/1.41 tff(7041,plain,
% 1.48/1.41 (succ(s83, s84) <=> succ(s83, s84)),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7042,axiom,(succ(s83, s84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound84')).
% 1.48/1.41 tff(7043,plain,
% 1.48/1.41 (succ(s83, s84)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7042, 7041])).
% 1.48/1.41 tff(7044,plain,
% 1.48/1.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7045,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7046,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7045, 7044])).
% 1.48/1.41 tff(7047,plain,
% 1.48/1.41 (trans(s83, s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7046, 7043, 39])).
% 1.48/1.41 tff(7048,plain,
% 1.48/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s83, s84)) | node14(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s83, s84)) | node14(s83, s84))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7049,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s83, s84)) | node14(s83, s84))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7050,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s83, s84)) | node14(s83, s84)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7049, 7048])).
% 1.48/1.41 tff(7051,plain,
% 1.48/1.41 (node14(s83, s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7050, 7, 7047])).
% 1.48/1.41 tff(7052,plain,
% 1.48/1.41 (((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | node9(s83) | node8(s83) | node10(s83) | (~node14(s83, s84)) | m_main_v_state2(s84, 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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | node9(s83) | node8(s83) | node10(s83) | (~node14(s83, s84)) | m_main_v_state2(s84, c_c2))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7053,plain,
% 1.48/1.41 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | node9(s83) | node8(s83) | node10(s83) | (~node14(s83, s84)) | m_main_v_state2(s84, c_c2))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7054,plain,
% 1.48/1.41 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | node9(s83) | node8(s83) | node10(s83) | (~node14(s83, s84)) | m_main_v_state2(s84, c_c2)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7053, 7052])).
% 1.48/1.41 tff(7055,plain,
% 1.48/1.41 ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | node9(s83) | node8(s83) | node10(s83) | m_main_v_state2(s84, c_c2)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7054, 617, 7051])).
% 1.48/1.41 tff(7056,plain,
% 1.48/1.41 (m_main_v_state2(s84, c_c2)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7055, 7040, 7036, 7000, 6993, 6989])).
% 1.48/1.41 tff(7057,plain,
% 1.48/1.41 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s84, c_t2)) | (~m_main_v_state2(s84, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s84, c_t2)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7058,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s84, c_t2)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7059,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s84, c_t2)) | (~m_main_v_state2(s84, c_c2))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7058, 7057])).
% 1.48/1.41 tff(7060,plain,
% 1.48/1.41 (~m_main_v_state2(s84, c_t2)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7059, 260, 7056])).
% 1.48/1.41 tff(7061,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s84, c_t2) | (~node12(s84)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s84, c_t2) | (~node12(s84)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7062,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s84, c_t2) | (~node12(s84)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7063,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s84, c_t2) | (~node12(s84))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7062, 7061])).
% 1.48/1.41 tff(7064,plain,
% 1.48/1.41 (~node12(s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7063, 633, 7060])).
% 1.48/1.41 tff(7065,plain,
% 1.48/1.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s83, s84)) | node7(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s83, s84)) | node7(s83, s84))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7066,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s83, s84)) | node7(s83, s84))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7067,plain,
% 1.48/1.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s83, s84)) | node7(s83, s84)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7066, 7065])).
% 1.48/1.41 tff(7068,plain,
% 1.48/1.41 (node7(s83, s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7067, 206, 7047])).
% 1.48/1.41 tff(7069,plain,
% 1.48/1.41 (((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, 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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, c_t1))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7070,plain,
% 1.48/1.41 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, c_t1))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7071,plain,
% 1.48/1.41 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node7(s83, s84)) | m_main_v_state1(s84, c_t1)),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7070, 7069])).
% 1.48/1.41 tff(7072,plain,
% 1.48/1.41 ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | m_main_v_state1(s84, c_t1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7071, 651, 7068])).
% 1.48/1.41 tff(7073,plain,
% 1.48/1.41 (m_main_v_state1(s84, c_t1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7072, 7000, 7036])).
% 1.48/1.41 tff(7074,plain,
% 1.48/1.41 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s84, c_n1)) | (~m_main_v_state1(s84, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s84, c_n1)) | (~m_main_v_state1(s84, c_t1)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7075,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s84, c_n1)) | (~m_main_v_state1(s84, c_t1)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7076,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s84, c_n1)) | (~m_main_v_state1(s84, c_t1))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7075, 7074])).
% 1.48/1.41 tff(7077,plain,
% 1.48/1.41 (~m_main_v_state1(s84, c_n1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7076, 17, 7073])).
% 1.48/1.41 tff(7078,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s84, c_n1) | (~node11(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s84, c_n1) | (~node11(s84)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7079,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s84, c_n1) | (~node11(s84)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7080,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s84, c_n1) | (~node11(s84))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7079, 7078])).
% 1.48/1.41 tff(7081,plain,
% 1.48/1.41 (~node11(s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7080, 238, 7077])).
% 1.48/1.41 tff(7082,plain,
% 1.48/1.41 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s84, c_t1)) | (~m_main_v_state1(s84, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s84, c_t1)) | (~m_main_v_state1(s84, c_c1)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7083,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s84, c_t1)) | (~m_main_v_state1(s84, c_c1)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7084,plain,
% 1.48/1.41 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s84, c_t1)) | (~m_main_v_state1(s84, c_c1))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 1.48/1.41 tff(7085,plain,
% 1.48/1.41 (~m_main_v_state1(s84, c_c1)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7084, 539, 7073])).
% 1.48/1.41 tff(7086,plain,
% 1.48/1.41 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s84, c_c1) | (~node10(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s84, c_c1) | (~node10(s84)))),
% 1.48/1.41 inference(rewrite,[status(thm)],[])).
% 1.48/1.41 tff(7087,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s84, c_c1) | (~node10(s84)))),
% 1.48/1.41 inference(quant_inst,[status(thm)],[])).
% 1.48/1.41 tff(7088,plain,
% 1.48/1.41 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s84, c_c1) | (~node10(s84))),
% 1.48/1.41 inference(modus_ponens,[status(thm)],[7087, 7086])).
% 1.48/1.41 tff(7089,plain,
% 1.48/1.41 (~node10(s84)),
% 1.48/1.41 inference(unit_resolution,[status(thm)],[7088, 675, 7085])).
% 1.48/1.42 tff(7090,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s84, c_n1) | (~node9(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s84, c_n1) | (~node9(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7091,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s84, c_n1) | (~node9(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7092,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s84, c_n1) | (~node9(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7091, 7090])).
% 1.48/1.42 tff(7093,plain,
% 1.48/1.42 (~node9(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7092, 686, 7077])).
% 1.48/1.42 tff(7094,plain,
% 1.48/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s84, c_n2)) | (~m_main_v_state2(s84, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s84, c_n2)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7095,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s84, c_n2)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7096,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s84, c_n2)) | (~m_main_v_state2(s84, c_c2))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7095, 7094])).
% 1.48/1.42 tff(7097,plain,
% 1.48/1.42 (~m_main_v_state2(s84, c_n2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7096, 697, 7056])).
% 1.48/1.42 tff(7098,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s84, c_n2) | (~node8(s84)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s84, c_n2) | (~node8(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7099,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s84, c_n2) | (~node8(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7100,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s84, c_n2) | (~node8(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7099, 7098])).
% 1.48/1.42 tff(7101,plain,
% 1.48/1.42 (~node8(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7100, 271, 7097])).
% 1.48/1.42 tff(7102,plain,
% 1.48/1.42 (succ(s84, s85) <=> succ(s84, s85)),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7103,axiom,(succ(s84, s85)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound85')).
% 1.48/1.42 tff(7104,plain,
% 1.48/1.42 (succ(s84, s85)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7103, 7102])).
% 1.48/1.42 tff(7105,plain,
% 1.48/1.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7106,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7107,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 1.48/1.42 tff(7108,plain,
% 1.48/1.42 (trans(s84, s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7107, 7104, 39])).
% 1.48/1.42 tff(7109,plain,
% 1.48/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s84, s85)) | node14(s84, s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s84, s85)) | node14(s84, s85))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7110,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s84, s85)) | node14(s84, s85))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7111,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s84, s85)) | node14(s84, s85)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7110, 7109])).
% 1.48/1.42 tff(7112,plain,
% 1.48/1.42 (node14(s84, s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7111, 7, 7108])).
% 1.48/1.42 tff(7113,plain,
% 1.48/1.42 (((~![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(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, 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(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7114,plain,
% 1.48/1.42 (((~m_main_v_state2(s84, c_c2)) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | m_main_v_state2(s85, c_n2)) <=> (m_main_v_state2(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7115,plain,
% 1.48/1.42 (((~![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(s84, c_c2)) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | m_main_v_state2(s85, 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(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2))))),
% 1.48/1.42 inference(monotonicity,[status(thm)],[7114])).
% 1.48/1.42 tff(7116,plain,
% 1.48/1.42 (((~![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(s84, c_c2)) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | m_main_v_state2(s85, 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(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2)))),
% 1.48/1.42 inference(transitivity,[status(thm)],[7115, 7113])).
% 1.48/1.42 tff(7117,plain,
% 1.48/1.42 ((~![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(s84, c_c2)) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | m_main_v_state2(s85, c_n2))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7118,plain,
% 1.48/1.42 ((~![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(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~node14(s84, s85)) | (~m_main_v_state2(s84, c_c2))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7117, 7116])).
% 1.48/1.42 tff(7119,plain,
% 1.48/1.42 (m_main_v_state2(s85, c_n2) | node9(s84) | node8(s84) | node10(s84) | node11(s84) | node12(s84) | (~m_main_v_state2(s84, c_c2))),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7118, 726, 7112])).
% 1.48/1.42 tff(7120,plain,
% 1.48/1.42 (m_main_v_state2(s85, c_n2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7119, 7101, 7056, 7093, 7089, 7081, 7064])).
% 1.48/1.42 tff(7121,plain,
% 1.48/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_c2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7122,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_c2)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7123,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_c2))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7122, 7121])).
% 1.48/1.42 tff(7124,plain,
% 1.48/1.42 (~m_main_v_state2(s85, c_c2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7123, 697, 7120])).
% 1.48/1.42 tff(7125,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s85, c_c2) | (~node3(s85)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s85, c_c2) | (~node3(s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7126,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s85, c_c2) | (~node3(s85)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7127,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s85, c_c2) | (~node3(s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7126, 7125])).
% 1.48/1.42 tff(7128,plain,
% 1.48/1.42 (~node3(s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7127, 399, 7124])).
% 1.48/1.42 tff(7129,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s84, c_n1) | (~node1(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s84, c_n1) | (~node1(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7130,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s84, c_n1) | (~node1(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7131,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s84, c_n1) | (~node1(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7130, 7129])).
% 1.48/1.42 tff(7132,plain,
% 1.48/1.42 (~node1(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7131, 421, 7077])).
% 1.48/1.42 tff(7133,plain,
% 1.48/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s83, s84)) | node18(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s83, s84)) | node18(s83, s84))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7134,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s83, s84)) | node18(s83, s84))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7135,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s83, s84)) | node18(s83, s84)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7134, 7133])).
% 1.48/1.42 tff(7136,plain,
% 1.48/1.42 (node18(s83, s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7135, 125, 7047])).
% 1.48/1.42 tff(7137,plain,
% 1.48/1.42 (((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, 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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, c_2))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7138,plain,
% 1.48/1.42 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, c_2))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7139,plain,
% 1.48/1.42 ((~![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(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | (~node18(s83, s84)) | m_main_v_turn(s84, c_2)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7138, 7137])).
% 1.48/1.42 tff(7140,plain,
% 1.48/1.42 ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state2(s83, c_t2)) | m_main_v_turn(s84, c_2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7139, 760, 7136])).
% 1.48/1.42 tff(7141,plain,
% 1.48/1.42 (m_main_v_turn(s84, c_2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7140, 7000, 7036])).
% 1.48/1.42 tff(7142,plain,
% 1.48/1.42 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s84, c_1)) | (~m_main_v_turn(s84, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s84, c_1)) | (~m_main_v_turn(s84, c_2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7143,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s84, c_1)) | (~m_main_v_turn(s84, c_2)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7144,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s84, c_1)) | (~m_main_v_turn(s84, c_2))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7143, 7142])).
% 1.48/1.42 tff(7145,plain,
% 1.48/1.42 (~m_main_v_turn(s84, c_1)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7144, 156, 7141])).
% 1.48/1.42 tff(7146,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s84, c_1) | (~node5(s84)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s84, c_1) | (~node5(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7147,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s84, c_1) | (~node5(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7148,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s84, c_1) | (~node5(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7147, 7146])).
% 1.48/1.42 tff(7149,plain,
% 1.48/1.42 (~node5(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7148, 776, 7145])).
% 1.48/1.42 tff(7150,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s84, c_n1) | (~node2(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s84, c_n1) | (~node2(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7151,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s84, c_n1) | (~node2(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7152,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s84, c_n1) | (~node2(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7151, 7150])).
% 1.48/1.42 tff(7153,plain,
% 1.48/1.42 (~node2(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7152, 787, 7077])).
% 1.48/1.42 tff(7154,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s84, c_n1) | (~node3(s84)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s84, c_n1) | (~node3(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7155,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s84, c_n1) | (~node3(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7156,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s84, c_n1) | (~node3(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 1.48/1.42 tff(7157,plain,
% 1.48/1.42 (~node3(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7156, 798, 7077])).
% 1.48/1.42 tff(7158,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s84, c_n2) | (~node4(s84)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s84, c_n2) | (~node4(s84)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7159,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s84, c_n2) | (~node4(s84)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7160,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s84, c_n2) | (~node4(s84))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7159, 7158])).
% 1.48/1.42 tff(7161,plain,
% 1.48/1.42 (~node4(s84)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7160, 388, 7097])).
% 1.48/1.42 tff(7162,plain,
% 1.48/1.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s84, s85)) | node7(s84, s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s84, s85)) | node7(s84, s85))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7163,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s84, s85)) | node7(s84, s85))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7164,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s84, s85)) | node7(s84, s85)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.48/1.42 tff(7165,plain,
% 1.48/1.42 (node7(s84, s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7164, 206, 7108])).
% 1.48/1.42 tff(7166,plain,
% 1.48/1.42 (((~![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(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85) | (~node7(s84, s85)))) <=> ((~![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(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85) | (~node7(s84, s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7167,plain,
% 1.48/1.42 ((~![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(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85) | (~node7(s84, s85)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7168,plain,
% 1.48/1.42 ((~![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(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85) | (~node7(s84, s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7167, 7166])).
% 1.48/1.42 tff(7169,plain,
% 1.48/1.42 (m_main_v_state1(s84, c_c1) | node1(s84) | node2(s84) | node3(s84) | node4(s84) | node5(s84) | node6(s84, s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7168, 820, 7165])).
% 1.48/1.42 tff(7170,plain,
% 1.48/1.42 (node6(s84, s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7169, 7161, 7085, 7157, 7153, 7149, 7132])).
% 1.48/1.42 tff(7171,plain,
% 1.48/1.42 (((~![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(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85)))) <=> ((~![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(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7172,plain,
% 1.48/1.42 (((~node6(s84, s85)) | m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, c_n1))) <=> (m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7173,plain,
% 1.48/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s84, s85)) | m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, 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(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85))))),
% 1.48/1.42 inference(monotonicity,[status(thm)],[7172])).
% 1.48/1.42 tff(7174,plain,
% 1.48/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s84, s85)) | m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, 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(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85)))),
% 1.48/1.42 inference(transitivity,[status(thm)],[7173, 7171])).
% 1.48/1.42 tff(7175,plain,
% 1.48/1.42 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s84, s85)) | m_main_v_state1(s84, c_n1) | (~m_main_v_state1(s85, c_n1)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7176,plain,
% 1.48/1.42 ((~![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(s84, c_n1) | (~m_main_v_state1(s85, c_n1)) | (~node6(s84, s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7175, 7174])).
% 1.48/1.42 tff(7177,plain,
% 1.48/1.42 (~m_main_v_state1(s85, c_n1)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7176, 835, 7077, 7170])).
% 1.48/1.42 tff(7178,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s85, c_n1) | (~node2(s85)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s85, c_n1) | (~node2(s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7179,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s85, c_n1) | (~node2(s85)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7180,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s85, c_n1) | (~node2(s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7179, 7178])).
% 1.48/1.42 tff(7181,plain,
% 1.48/1.42 (~node2(s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7180, 787, 7177])).
% 1.48/1.42 tff(7182,plain,
% 1.48/1.42 (((~![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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85)))) <=> ((~![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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7183,plain,
% 1.48/1.42 (((~node6(s84, s85)) | (~m_main_v_state1(s84, c_t1)) | m_main_v_state1(s85, c_t1)) <=> ((~m_main_v_state1(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7184,plain,
% 1.48/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s84, s85)) | (~m_main_v_state1(s84, c_t1)) | m_main_v_state1(s85, 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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85))))),
% 1.48/1.42 inference(monotonicity,[status(thm)],[7183])).
% 1.48/1.42 tff(7185,plain,
% 1.48/1.42 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s84, s85)) | (~m_main_v_state1(s84, c_t1)) | m_main_v_state1(s85, 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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85)))),
% 1.48/1.42 inference(transitivity,[status(thm)],[7184, 7182])).
% 1.48/1.42 tff(7186,plain,
% 1.48/1.42 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s84, s85)) | (~m_main_v_state1(s84, c_t1)) | m_main_v_state1(s85, c_t1))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7187,plain,
% 1.48/1.42 ((~![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(s84, c_t1)) | m_main_v_state1(s85, c_t1) | (~node6(s84, s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7186, 7185])).
% 1.48/1.42 tff(7188,plain,
% 1.48/1.42 (m_main_v_state1(s85, c_t1)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7187, 856, 7073, 7170])).
% 1.48/1.42 tff(7189,plain,
% 1.48/1.42 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_t2)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7190,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_t2)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7191,plain,
% 1.48/1.42 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s85, c_n2)) | (~m_main_v_state2(s85, c_t2))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7190, 7189])).
% 1.48/1.42 tff(7192,plain,
% 1.48/1.42 (~m_main_v_state2(s85, c_t2)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7191, 77, 7120])).
% 1.48/1.42 tff(7193,plain,
% 1.48/1.42 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s85, c_t2) | (~node1(s85)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s85, c_t2) | (~node1(s85)))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7194,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s85, c_t2) | (~node1(s85)))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7195,plain,
% 1.48/1.42 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s85, c_t2) | (~node1(s85))),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7194, 7193])).
% 1.48/1.42 tff(7196,plain,
% 1.48/1.42 (~node1(s85)),
% 1.48/1.42 inference(unit_resolution,[status(thm)],[7195, 195, 7192])).
% 1.48/1.42 tff(7197,plain,
% 1.48/1.42 (succ(s85, s86) <=> succ(s85, s86)),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7198,axiom,(succ(s85, s86)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound86')).
% 1.48/1.42 tff(7199,plain,
% 1.48/1.42 (succ(s85, s86)),
% 1.48/1.42 inference(modus_ponens,[status(thm)],[7198, 7197])).
% 1.48/1.42 tff(7200,plain,
% 1.48/1.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86))),
% 1.48/1.42 inference(rewrite,[status(thm)],[])).
% 1.48/1.42 tff(7201,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))),
% 1.48/1.42 inference(quant_inst,[status(thm)],[])).
% 1.48/1.42 tff(7202,plain,
% 1.48/1.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7201, 7200])).
% 1.48/1.43 tff(7203,plain,
% 1.48/1.43 (trans(s85, s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7202, 7199, 39])).
% 1.48/1.43 tff(7204,plain,
% 1.48/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s85, s86)) | node7(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s85, s86)) | node7(s85, s86))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7205,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s85, s86)) | node7(s85, s86))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7206,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s85, s86)) | node7(s85, s86)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7205, 7204])).
% 1.48/1.43 tff(7207,plain,
% 1.48/1.43 (node7(s85, s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7206, 206, 7203])).
% 1.48/1.43 tff(7208,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)))) <=> ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7209,plain,
% 1.48/1.43 (((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)) | m_main_v_state1(s86, c_c1)) <=> ((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7210,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)) | m_main_v_state1(s86, 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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86))))),
% 1.48/1.43 inference(monotonicity,[status(thm)],[7209])).
% 1.48/1.43 tff(7211,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)) | m_main_v_state1(s86, 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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)))),
% 1.48/1.43 inference(transitivity,[status(thm)],[7210, 7208])).
% 1.48/1.43 tff(7212,plain,
% 1.48/1.43 ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86)) | m_main_v_state1(s86, c_c1))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7213,plain,
% 1.48/1.43 ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85) | (~node7(s85, s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 1.48/1.43 tff(7214,plain,
% 1.48/1.43 ((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state1(s86, c_c1) | node1(s85) | node2(s85) | node3(s85)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7213, 892, 7207])).
% 1.48/1.43 tff(7215,plain,
% 1.48/1.43 (m_main_v_state1(s86, c_c1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7214, 7196, 7120, 7188, 7181, 7128])).
% 1.48/1.43 tff(7216,plain,
% 1.48/1.43 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s86, c_t1)) | (~m_main_v_state1(s86, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s86, c_t1)) | (~m_main_v_state1(s86, c_c1)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7217,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s86, c_t1)) | (~m_main_v_state1(s86, c_c1)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7218,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s86, c_t1)) | (~m_main_v_state1(s86, c_c1))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7217, 7216])).
% 1.48/1.43 tff(7219,plain,
% 1.48/1.43 (~m_main_v_state1(s86, c_t1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7218, 539, 7215])).
% 1.48/1.43 tff(7220,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s86, c_t1) | (~node5(s86)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s86, c_t1) | (~node5(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7221,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s86, c_t1) | (~node5(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7222,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s86, c_t1) | (~node5(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 1.48/1.43 tff(7223,plain,
% 1.48/1.43 (~node5(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7222, 550, 7219])).
% 1.48/1.43 tff(7224,plain,
% 1.48/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s85, s86)) | node14(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s85, s86)) | node14(s85, s86))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7225,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s85, s86)) | node14(s85, s86))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7226,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s85, s86)) | node14(s85, s86)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7225, 7224])).
% 1.48/1.43 tff(7227,plain,
% 1.48/1.43 (node14(s85, s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7226, 7, 7203])).
% 1.48/1.43 tff(7228,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | (~node14(s85, s86)) | m_main_v_state2(s86, 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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | (~node14(s85, s86)) | m_main_v_state2(s86, c_t2))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7229,plain,
% 1.48/1.43 ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | (~node14(s85, s86)) | m_main_v_state2(s86, c_t2))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7230,plain,
% 1.48/1.43 ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | (~node14(s85, s86)) | m_main_v_state2(s86, c_t2)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7229, 7228])).
% 1.48/1.43 tff(7231,plain,
% 1.48/1.43 ((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_state2(s86, c_t2)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7230, 922, 7227])).
% 1.48/1.43 tff(7232,plain,
% 1.48/1.43 (m_main_v_state2(s86, c_t2)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7231, 7188, 7120])).
% 1.48/1.43 tff(7233,plain,
% 1.48/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s86, c_n2)) | (~m_main_v_state2(s86, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s86, c_n2)) | (~m_main_v_state2(s86, c_t2)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7234,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s86, c_n2)) | (~m_main_v_state2(s86, c_t2)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7235,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s86, c_n2)) | (~m_main_v_state2(s86, c_t2))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 1.48/1.43 tff(7236,plain,
% 1.48/1.43 (~m_main_v_state2(s86, c_n2)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7235, 77, 7232])).
% 1.48/1.43 tff(7237,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s86, c_n2) | (~node4(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s86, c_n2) | (~node4(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7238,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s86, c_n2) | (~node4(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7239,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s86, c_n2) | (~node4(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7238, 7237])).
% 1.48/1.43 tff(7240,plain,
% 1.48/1.43 (~node4(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7239, 388, 7236])).
% 1.48/1.43 tff(7241,plain,
% 1.48/1.43 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s86, c_t2)) | (~m_main_v_state2(s86, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s86, c_t2)) | (~m_main_v_state2(s86, c_c2)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7242,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s86, c_t2)) | (~m_main_v_state2(s86, c_c2)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7243,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s86, c_t2)) | (~m_main_v_state2(s86, c_c2))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 1.48/1.43 tff(7244,plain,
% 1.48/1.43 (~m_main_v_state2(s86, c_c2)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7243, 260, 7232])).
% 1.48/1.43 tff(7245,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s86, c_c2) | (~node3(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s86, c_c2) | (~node3(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7246,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s86, c_c2) | (~node3(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7247,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s86, c_c2) | (~node3(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7246, 7245])).
% 1.48/1.43 tff(7248,plain,
% 1.48/1.43 (~node3(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7247, 399, 7244])).
% 1.48/1.43 tff(7249,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s86, c_n2) | (~node2(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s86, c_n2) | (~node2(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7250,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s86, c_n2) | (~node2(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7251,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s86, c_n2) | (~node2(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7250, 7249])).
% 1.48/1.43 tff(7252,plain,
% 1.48/1.43 (~node2(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7251, 410, 7236])).
% 1.48/1.43 tff(7253,plain,
% 1.48/1.43 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s86, c_n1)) | (~m_main_v_state1(s86, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s86, c_n1)) | (~m_main_v_state1(s86, c_c1)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7254,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s86, c_n1)) | (~m_main_v_state1(s86, c_c1)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7255,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s86, c_n1)) | (~m_main_v_state1(s86, c_c1))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7254, 7253])).
% 1.48/1.43 tff(7256,plain,
% 1.48/1.43 (~m_main_v_state1(s86, c_n1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7255, 454, 7215])).
% 1.48/1.43 tff(7257,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s86, c_n1) | (~node1(s86)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s86, c_n1) | (~node1(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7258,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s86, c_n1) | (~node1(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7259,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s86, c_n1) | (~node1(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7258, 7257])).
% 1.48/1.43 tff(7260,plain,
% 1.48/1.43 (~node1(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7259, 421, 7256])).
% 1.48/1.43 tff(7261,plain,
% 1.48/1.43 (succ(s86, s87) <=> succ(s86, s87)),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7262,axiom,(succ(s86, s87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound87')).
% 1.48/1.43 tff(7263,plain,
% 1.48/1.43 (succ(s86, s87)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7262, 7261])).
% 1.48/1.43 tff(7264,plain,
% 1.48/1.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7265,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7266,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7265, 7264])).
% 1.48/1.43 tff(7267,plain,
% 1.48/1.43 (trans(s86, s87)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7266, 7263, 39])).
% 1.48/1.43 tff(7268,plain,
% 1.48/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s86, s87)) | node7(s86, s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s86, s87)) | node7(s86, s87))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7269,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s86, s87)) | node7(s86, s87))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7270,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s86, s87)) | node7(s86, s87)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7269, 7268])).
% 1.48/1.43 tff(7271,plain,
% 1.48/1.43 (node7(s86, s87)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7270, 206, 7267])).
% 1.48/1.43 tff(7272,plain,
% 1.48/1.43 (((~![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(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)))) <=> ((~![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(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7273,plain,
% 1.48/1.43 (((~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)) | m_main_v_state1(s87, c_n1)) <=> (m_main_v_state1(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7274,plain,
% 1.48/1.43 (((~![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(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)) | m_main_v_state1(s87, 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(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87))))),
% 1.48/1.43 inference(monotonicity,[status(thm)],[7273])).
% 1.48/1.43 tff(7275,plain,
% 1.48/1.43 (((~![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(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)) | m_main_v_state1(s87, 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(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)))),
% 1.48/1.43 inference(transitivity,[status(thm)],[7274, 7272])).
% 1.48/1.43 tff(7276,plain,
% 1.48/1.43 ((~![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(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87)) | m_main_v_state1(s87, c_n1))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7277,plain,
% 1.48/1.43 ((~![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(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86) | (~node7(s86, s87))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7276, 7275])).
% 1.48/1.43 tff(7278,plain,
% 1.48/1.43 (m_main_v_state1(s87, c_n1) | (~m_main_v_state1(s86, c_c1)) | node1(s86) | node2(s86) | node3(s86) | node4(s86) | node5(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7277, 584, 7271])).
% 1.48/1.43 tff(7279,plain,
% 1.48/1.43 (m_main_v_state1(s87, c_n1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7278, 7260, 7215, 7252, 7248, 7240, 7223])).
% 1.48/1.43 tff(7280,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s85, c_t2) | (~node15(s85)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s85, c_t2) | (~node15(s85)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7281,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s85, c_t2) | (~node15(s85)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7282,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s85, c_t2) | (~node15(s85))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7281, 7280])).
% 1.48/1.43 tff(7283,plain,
% 1.48/1.43 (~node15(s85)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7282, 103, 7192])).
% 1.48/1.43 tff(7284,plain,
% 1.48/1.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s85, s86)) | node18(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s85, s86)) | node18(s85, s86))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7285,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s85, s86)) | node18(s85, s86))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7286,plain,
% 1.48/1.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s85, s86)) | node18(s85, s86)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 1.48/1.43 tff(7287,plain,
% 1.48/1.43 (node18(s85, s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7286, 125, 7203])).
% 1.48/1.43 tff(7288,plain,
% 1.48/1.43 (((~![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(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, 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(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7289,plain,
% 1.48/1.43 (((~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node15(s85) | (~node18(s85, s86)) | m_main_v_turn(s86, c_1)) <=> (node15(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7290,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node15(s85) | (~node18(s85, s86)) | m_main_v_turn(s86, 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(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1)))),
% 1.48/1.43 inference(monotonicity,[status(thm)],[7289])).
% 1.48/1.43 tff(7291,plain,
% 1.48/1.43 (((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node15(s85) | (~node18(s85, s86)) | m_main_v_turn(s86, 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(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1))),
% 1.48/1.43 inference(transitivity,[status(thm)],[7290, 7288])).
% 1.48/1.43 tff(7292,plain,
% 1.48/1.43 ((~![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(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | node15(s85) | (~node18(s85, s86)) | m_main_v_turn(s86, c_1))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7293,plain,
% 1.48/1.43 ((~![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(s85) | (~node18(s85, s86)) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1)),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7292, 7291])).
% 1.48/1.43 tff(7294,plain,
% 1.48/1.43 (node15(s85) | (~m_main_v_state1(s85, c_t1)) | (~m_main_v_state2(s85, c_n2)) | m_main_v_turn(s86, c_1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7293, 992, 7287])).
% 1.48/1.43 tff(7295,plain,
% 1.48/1.43 (m_main_v_turn(s86, c_1)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7294, 7283, 7120, 7188])).
% 1.48/1.43 tff(7296,plain,
% 1.48/1.43 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s86, c_1)) | (~m_main_v_turn(s86, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s86, c_1)) | (~m_main_v_turn(s86, c_2)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7297,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s86, c_1)) | (~m_main_v_turn(s86, c_2)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7298,plain,
% 1.48/1.43 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s86, c_1)) | (~m_main_v_turn(s86, c_2))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7297, 7296])).
% 1.48/1.43 tff(7299,plain,
% 1.48/1.43 (~m_main_v_turn(s86, c_2)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7298, 156, 7295])).
% 1.48/1.43 tff(7300,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s86, c_2) | (~node12(s86)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s86, c_2) | (~node12(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7301,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s86, c_2) | (~node12(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7302,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s86, c_2) | (~node12(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7301, 7300])).
% 1.48/1.43 tff(7303,plain,
% 1.48/1.43 (~node12(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7302, 184, 7299])).
% 1.48/1.43 tff(7304,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s86, c_n2) | (~node8(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s86, c_n2) | (~node8(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7305,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s86, c_n2) | (~node8(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7306,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s86, c_n2) | (~node8(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7305, 7304])).
% 1.48/1.43 tff(7307,plain,
% 1.48/1.43 (~node8(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7306, 271, 7236])).
% 1.48/1.43 tff(7308,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s86, c_n2) | (~node9(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s86, c_n2) | (~node9(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7309,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s86, c_n2) | (~node9(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7310,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s86, c_n2) | (~node9(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7309, 7308])).
% 1.48/1.43 tff(7311,plain,
% 1.48/1.43 (~node9(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7310, 88, 7236])).
% 1.48/1.43 tff(7312,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s86, c_n2) | (~node10(s86)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s86, c_n2) | (~node10(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7313,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s86, c_n2) | (~node10(s86)))),
% 1.48/1.43 inference(quant_inst,[status(thm)],[])).
% 1.48/1.43 tff(7314,plain,
% 1.48/1.43 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s86, c_n2) | (~node10(s86))),
% 1.48/1.43 inference(modus_ponens,[status(thm)],[7313, 7312])).
% 1.48/1.43 tff(7315,plain,
% 1.48/1.43 (~node10(s86)),
% 1.48/1.43 inference(unit_resolution,[status(thm)],[7314, 249, 7236])).
% 1.48/1.43 tff(7316,plain,
% 1.48/1.43 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s86, c_n1) | (~node11(s86)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s86, c_n1) | (~node11(s86)))),
% 1.48/1.43 inference(rewrite,[status(thm)],[])).
% 1.48/1.43 tff(7317,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s86, c_n1) | (~node11(s86)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7318,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s86, c_n1) | (~node11(s86))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7317, 7316])).
% 1.48/1.44 tff(7319,plain,
% 1.48/1.44 (~node11(s86)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7318, 238, 7256])).
% 1.48/1.44 tff(7320,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s86, s87)) | node14(s86, s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s86, s87)) | node14(s86, s87))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7321,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s86, s87)) | node14(s86, s87))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7322,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s86, s87)) | node14(s86, s87)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 1.48/1.44 tff(7323,plain,
% 1.48/1.44 (node14(s86, s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7322, 7, 7267])).
% 1.48/1.44 tff(7324,plain,
% 1.48/1.44 (((~![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(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87) | (~node14(s86, s87)))) <=> ((~![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(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87) | (~node14(s86, s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7325,plain,
% 1.48/1.44 ((~![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(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87) | (~node14(s86, s87)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7326,plain,
% 1.48/1.44 ((~![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(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87) | (~node14(s86, s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7325, 7324])).
% 1.48/1.44 tff(7327,plain,
% 1.48/1.44 (m_main_v_state2(s86, c_c2) | node9(s86) | node8(s86) | node10(s86) | node11(s86) | node12(s86) | node13(s86, s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7326, 296, 7323])).
% 1.48/1.44 tff(7328,plain,
% 1.48/1.44 (node13(s86, s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7327, 7319, 7244, 7315, 7311, 7307, 7303])).
% 1.48/1.44 tff(7329,plain,
% 1.48/1.44 (((~![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(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87)))) <=> ((~![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(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7330,plain,
% 1.48/1.44 (((~node13(s86, s87)) | (~m_main_v_state2(s86, c_t2)) | m_main_v_state2(s87, c_t2)) <=> ((~m_main_v_state2(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7331,plain,
% 1.48/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s86, s87)) | (~m_main_v_state2(s86, c_t2)) | m_main_v_state2(s87, 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(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87))))),
% 1.48/1.44 inference(monotonicity,[status(thm)],[7330])).
% 1.48/1.44 tff(7332,plain,
% 1.48/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s86, s87)) | (~m_main_v_state2(s86, c_t2)) | m_main_v_state2(s87, 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(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87)))),
% 1.48/1.44 inference(transitivity,[status(thm)],[7331, 7329])).
% 1.48/1.44 tff(7333,plain,
% 1.48/1.44 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s86, s87)) | (~m_main_v_state2(s86, c_t2)) | m_main_v_state2(s87, c_t2))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7334,plain,
% 1.48/1.44 ((~![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(s86, c_t2)) | m_main_v_state2(s87, c_t2) | (~node13(s86, s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7333, 7332])).
% 1.48/1.44 tff(7335,plain,
% 1.48/1.44 (m_main_v_state2(s87, c_t2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7334, 518, 7232, 7328])).
% 1.48/1.44 tff(7336,plain,
% 1.48/1.44 (succ(s87, s88) <=> succ(s87, s88)),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7337,axiom,(succ(s87, s88)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound88')).
% 1.48/1.44 tff(7338,plain,
% 1.48/1.44 (succ(s87, s88)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7337, 7336])).
% 1.48/1.44 tff(7339,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7340,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7341,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7340, 7339])).
% 1.48/1.44 tff(7342,plain,
% 1.48/1.44 (trans(s87, s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7341, 7338, 39])).
% 1.48/1.44 tff(7343,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s87, s88)) | node7(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s87, s88)) | node7(s87, s88))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7344,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s87, s88)) | node7(s87, s88))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7345,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s87, s88)) | node7(s87, s88)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 1.48/1.44 tff(7346,plain,
% 1.48/1.44 (node7(s87, s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7345, 206, 7342])).
% 1.48/1.44 tff(7347,plain,
% 1.48/1.44 (((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node7(s87, s88)) | m_main_v_state1(s88, 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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node7(s87, s88)) | m_main_v_state1(s88, c_t1))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7348,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node7(s87, s88)) | m_main_v_state1(s88, c_t1))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7349,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node7(s87, s88)) | m_main_v_state1(s88, c_t1)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7348, 7347])).
% 1.48/1.44 tff(7350,plain,
% 1.48/1.44 ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | m_main_v_state1(s88, c_t1)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7349, 651, 7346])).
% 1.48/1.44 tff(7351,plain,
% 1.48/1.44 (m_main_v_state1(s88, c_t1)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7350, 7335, 7279])).
% 1.48/1.44 tff(7352,plain,
% 1.48/1.44 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s88, c_n1)) | (~m_main_v_state1(s88, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s88, c_n1)) | (~m_main_v_state1(s88, c_t1)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7353,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s88, c_n1)) | (~m_main_v_state1(s88, c_t1)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7354,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s88, c_n1)) | (~m_main_v_state1(s88, c_t1))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7353, 7352])).
% 1.48/1.44 tff(7355,plain,
% 1.48/1.44 (~m_main_v_state1(s88, c_n1)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7354, 17, 7351])).
% 1.48/1.44 tff(7356,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s88, c_n1) | (~node1(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s88, c_n1) | (~node1(s88)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7357,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s88, c_n1) | (~node1(s88)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7358,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s88, c_n1) | (~node1(s88))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 1.48/1.44 tff(7359,plain,
% 1.48/1.44 (~node1(s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7358, 421, 7355])).
% 1.48/1.44 tff(7360,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s87, s88)) | node18(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s87, s88)) | node18(s87, s88))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7361,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s87, s88)) | node18(s87, s88))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7362,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s87, s88)) | node18(s87, s88)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7361, 7360])).
% 1.48/1.44 tff(7363,plain,
% 1.48/1.44 (node18(s87, s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7362, 125, 7342])).
% 1.48/1.44 tff(7364,plain,
% 1.48/1.44 (((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node18(s87, s88)) | m_main_v_turn(s88, 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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node18(s87, s88)) | m_main_v_turn(s88, c_2))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7365,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node18(s87, s88)) | m_main_v_turn(s88, c_2))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7366,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | (~node18(s87, s88)) | m_main_v_turn(s88, c_2)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7365, 7364])).
% 1.48/1.44 tff(7367,plain,
% 1.48/1.44 ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | m_main_v_turn(s88, c_2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7366, 760, 7363])).
% 1.48/1.44 tff(7368,plain,
% 1.48/1.44 (m_main_v_turn(s88, c_2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7367, 7335, 7279])).
% 1.48/1.44 tff(7369,plain,
% 1.48/1.44 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s88, c_1)) | (~m_main_v_turn(s88, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s88, c_1)) | (~m_main_v_turn(s88, c_2)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7370,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s88, c_1)) | (~m_main_v_turn(s88, c_2)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7371,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s88, c_1)) | (~m_main_v_turn(s88, c_2))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7370, 7369])).
% 1.48/1.44 tff(7372,plain,
% 1.48/1.44 (~m_main_v_turn(s88, c_1)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7371, 156, 7368])).
% 1.48/1.44 tff(7373,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s88, c_1) | (~node5(s88)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s88, c_1) | (~node5(s88)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7374,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s88, c_1) | (~node5(s88)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7375,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s88, c_1) | (~node5(s88))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7374, 7373])).
% 1.48/1.44 tff(7376,plain,
% 1.48/1.44 (~node5(s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7375, 776, 7372])).
% 1.48/1.44 tff(7377,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s88, c_n1) | (~node2(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s88, c_n1) | (~node2(s88)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7378,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s88, c_n1) | (~node2(s88)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7379,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s88, c_n1) | (~node2(s88))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7378, 7377])).
% 1.48/1.44 tff(7380,plain,
% 1.48/1.44 (~node2(s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7379, 787, 7355])).
% 1.48/1.44 tff(7381,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s88, c_n1) | (~node3(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s88, c_n1) | (~node3(s88)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7382,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s88, c_n1) | (~node3(s88)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7383,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s88, c_n1) | (~node3(s88))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7382, 7381])).
% 1.48/1.44 tff(7384,plain,
% 1.48/1.44 (~node3(s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7383, 798, 7355])).
% 1.48/1.44 tff(7385,plain,
% 1.48/1.44 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s88, c_t1)) | (~m_main_v_state1(s88, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s88, c_t1)) | (~m_main_v_state1(s88, c_c1)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7386,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s88, c_t1)) | (~m_main_v_state1(s88, c_c1)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7387,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s88, c_t1)) | (~m_main_v_state1(s88, c_c1))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7386, 7385])).
% 1.48/1.44 tff(7388,plain,
% 1.48/1.44 (~m_main_v_state1(s88, c_c1)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7387, 539, 7351])).
% 1.48/1.44 tff(7389,plain,
% 1.48/1.44 (((~![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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87)))) <=> ((~![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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7390,plain,
% 1.48/1.44 (((~node13(s86, s87)) | m_main_v_state2(s86, c_n2) | (~m_main_v_state2(s87, c_n2))) <=> (m_main_v_state2(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7391,plain,
% 1.48/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s86, s87)) | m_main_v_state2(s86, c_n2) | (~m_main_v_state2(s87, 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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87))))),
% 1.48/1.44 inference(monotonicity,[status(thm)],[7390])).
% 1.48/1.44 tff(7392,plain,
% 1.48/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s86, s87)) | m_main_v_state2(s86, c_n2) | (~m_main_v_state2(s87, 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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87)))),
% 1.48/1.44 inference(transitivity,[status(thm)],[7391, 7389])).
% 1.48/1.44 tff(7393,plain,
% 1.48/1.44 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s86, s87)) | m_main_v_state2(s86, c_n2) | (~m_main_v_state2(s87, c_n2)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7394,plain,
% 1.48/1.44 ((~![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(s86, c_n2) | (~m_main_v_state2(s87, c_n2)) | (~node13(s86, s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7393, 7392])).
% 1.48/1.44 tff(7395,plain,
% 1.48/1.44 (~m_main_v_state2(s87, c_n2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7394, 311, 7236, 7328])).
% 1.48/1.44 tff(7396,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s87, c_n2) | (~node9(s87)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s87, c_n2) | (~node9(s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7397,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s87, c_n2) | (~node9(s87)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7398,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s87, c_n2) | (~node9(s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7397, 7396])).
% 1.48/1.44 tff(7399,plain,
% 1.48/1.44 (~node9(s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7398, 88, 7395])).
% 1.48/1.44 tff(7400,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s87, c_n2) | (~node10(s87)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s87, c_n2) | (~node10(s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7401,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s87, c_n2) | (~node10(s87)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7402,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s87, c_n2) | (~node10(s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7401, 7400])).
% 1.48/1.44 tff(7403,plain,
% 1.48/1.44 (~node10(s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7402, 249, 7395])).
% 1.48/1.44 tff(7404,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s87, c_n2) | (~node8(s87)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s87, c_n2) | (~node8(s87)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7405,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s87, c_n2) | (~node8(s87)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7406,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s87, c_n2) | (~node8(s87))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 1.48/1.44 tff(7407,plain,
% 1.48/1.44 (~node8(s87)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7406, 271, 7395])).
% 1.48/1.44 tff(7408,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s87, s88)) | node14(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s87, s88)) | node14(s87, s88))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7409,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s87, s88)) | node14(s87, s88))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7410,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s87, s88)) | node14(s87, s88)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7409, 7408])).
% 1.48/1.44 tff(7411,plain,
% 1.48/1.44 (node14(s87, s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7410, 7, 7342])).
% 1.48/1.44 tff(7412,plain,
% 1.48/1.44 (((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | node9(s87) | node8(s87) | node10(s87) | (~node14(s87, s88)) | m_main_v_state2(s88, 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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | node9(s87) | node8(s87) | node10(s87) | (~node14(s87, s88)) | m_main_v_state2(s88, c_c2))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7413,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | node9(s87) | node8(s87) | node10(s87) | (~node14(s87, s88)) | m_main_v_state2(s88, c_c2))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7414,plain,
% 1.48/1.44 ((~![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(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | node9(s87) | node8(s87) | node10(s87) | (~node14(s87, s88)) | m_main_v_state2(s88, c_c2)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7413, 7412])).
% 1.48/1.44 tff(7415,plain,
% 1.48/1.44 ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state2(s87, c_t2)) | node9(s87) | node8(s87) | node10(s87) | m_main_v_state2(s88, c_c2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7414, 617, 7411])).
% 1.48/1.44 tff(7416,plain,
% 1.48/1.44 (m_main_v_state2(s88, c_c2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7415, 7407, 7279, 7335, 7403, 7399])).
% 1.48/1.44 tff(7417,plain,
% 1.48/1.44 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s88, c_n2)) | (~m_main_v_state2(s88, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s88, c_n2)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7418,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s88, c_n2)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7419,plain,
% 1.48/1.44 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s88, c_n2)) | (~m_main_v_state2(s88, c_c2))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 1.48/1.44 tff(7420,plain,
% 1.48/1.44 (~m_main_v_state2(s88, c_n2)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7419, 697, 7416])).
% 1.48/1.44 tff(7421,plain,
% 1.48/1.44 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s88, c_n2) | (~node4(s88)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s88, c_n2) | (~node4(s88)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7422,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s88, c_n2) | (~node4(s88)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7423,plain,
% 1.48/1.44 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s88, c_n2) | (~node4(s88))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7422, 7421])).
% 1.48/1.44 tff(7424,plain,
% 1.48/1.44 (~node4(s88)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7423, 388, 7420])).
% 1.48/1.44 tff(7425,plain,
% 1.48/1.44 (succ(s88, s89) <=> succ(s88, s89)),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7426,axiom,(succ(s88, s89)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound89')).
% 1.48/1.44 tff(7427,plain,
% 1.48/1.44 (succ(s88, s89)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 1.48/1.44 tff(7428,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7429,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7430,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7429, 7428])).
% 1.48/1.44 tff(7431,plain,
% 1.48/1.44 (trans(s88, s89)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7430, 7427, 39])).
% 1.48/1.44 tff(7432,plain,
% 1.48/1.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s88, s89)) | node7(s88, s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s88, s89)) | node7(s88, s89))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7433,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s88, s89)) | node7(s88, s89))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7434,plain,
% 1.48/1.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s88, s89)) | node7(s88, s89)),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7433, 7432])).
% 1.48/1.44 tff(7435,plain,
% 1.48/1.44 (node7(s88, s89)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7434, 206, 7431])).
% 1.48/1.44 tff(7436,plain,
% 1.48/1.44 (((~![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(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89) | (~node7(s88, s89)))) <=> ((~![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(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89) | (~node7(s88, s89)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7437,plain,
% 1.48/1.44 ((~![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(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89) | (~node7(s88, s89)))),
% 1.48/1.44 inference(quant_inst,[status(thm)],[])).
% 1.48/1.44 tff(7438,plain,
% 1.48/1.44 ((~![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(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89) | (~node7(s88, s89))),
% 1.48/1.44 inference(modus_ponens,[status(thm)],[7437, 7436])).
% 1.48/1.44 tff(7439,plain,
% 1.48/1.44 (m_main_v_state1(s88, c_c1) | node1(s88) | node2(s88) | node3(s88) | node4(s88) | node5(s88) | node6(s88, s89)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7438, 820, 7435])).
% 1.48/1.44 tff(7440,plain,
% 1.48/1.44 (node6(s88, s89)),
% 1.48/1.44 inference(unit_resolution,[status(thm)],[7439, 7424, 7388, 7384, 7380, 7376, 7359])).
% 1.48/1.44 tff(7441,plain,
% 1.48/1.44 (((~![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(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89)))) <=> ((~![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(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7442,plain,
% 1.48/1.44 (((~node6(s88, s89)) | (~m_main_v_state1(s88, c_t1)) | m_main_v_state1(s89, c_t1)) <=> ((~m_main_v_state1(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89)))),
% 1.48/1.44 inference(rewrite,[status(thm)],[])).
% 1.48/1.44 tff(7443,plain,
% 1.48/1.44 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s88, s89)) | (~m_main_v_state1(s88, c_t1)) | m_main_v_state1(s89, 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(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89))))),
% 1.48/1.45 inference(monotonicity,[status(thm)],[7442])).
% 1.48/1.45 tff(7444,plain,
% 1.48/1.45 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s88, s89)) | (~m_main_v_state1(s88, c_t1)) | m_main_v_state1(s89, 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(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89)))),
% 1.48/1.45 inference(transitivity,[status(thm)],[7443, 7441])).
% 1.48/1.45 tff(7445,plain,
% 1.48/1.45 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s88, s89)) | (~m_main_v_state1(s88, c_t1)) | m_main_v_state1(s89, c_t1))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7446,plain,
% 1.48/1.45 ((~![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(s88, c_t1)) | m_main_v_state1(s89, c_t1) | (~node6(s88, s89))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7445, 7444])).
% 1.48/1.45 tff(7447,plain,
% 1.48/1.45 (m_main_v_state1(s89, c_t1)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7446, 856, 7351, 7440])).
% 1.48/1.45 tff(7448,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s88, c_t2)) | (~m_main_v_state2(s88, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s88, c_t2)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7449,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s88, c_t2)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7450,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s88, c_t2)) | (~m_main_v_state2(s88, c_c2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7449, 7448])).
% 1.48/1.45 tff(7451,plain,
% 1.48/1.45 (~m_main_v_state2(s88, c_t2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7450, 260, 7416])).
% 1.48/1.45 tff(7452,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s88, c_t2) | (~node12(s88)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s88, c_t2) | (~node12(s88)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7453,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s88, c_t2) | (~node12(s88)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7454,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s88, c_t2) | (~node12(s88))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 1.48/1.45 tff(7455,plain,
% 1.48/1.45 (~node12(s88)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7454, 633, 7451])).
% 1.48/1.45 tff(7456,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s88, c_n1) | (~node11(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s88, c_n1) | (~node11(s88)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7457,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s88, c_n1) | (~node11(s88)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7458,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s88, c_n1) | (~node11(s88))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7457, 7456])).
% 1.48/1.45 tff(7459,plain,
% 1.48/1.45 (~node11(s88)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7458, 238, 7355])).
% 1.48/1.45 tff(7460,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s88, c_c1) | (~node10(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s88, c_c1) | (~node10(s88)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7461,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s88, c_c1) | (~node10(s88)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7462,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s88, c_c1) | (~node10(s88))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7461, 7460])).
% 1.48/1.45 tff(7463,plain,
% 1.48/1.45 (~node10(s88)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7462, 675, 7388])).
% 1.48/1.45 tff(7464,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s88, c_n1) | (~node9(s88)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s88, c_n1) | (~node9(s88)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7465,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s88, c_n1) | (~node9(s88)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7466,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s88, c_n1) | (~node9(s88))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7465, 7464])).
% 1.48/1.45 tff(7467,plain,
% 1.48/1.45 (~node9(s88)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7466, 686, 7355])).
% 1.48/1.45 tff(7468,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s88, c_n2) | (~node8(s88)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s88, c_n2) | (~node8(s88)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7469,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s88, c_n2) | (~node8(s88)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7470,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s88, c_n2) | (~node8(s88))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7469, 7468])).
% 1.48/1.45 tff(7471,plain,
% 1.48/1.45 (~node8(s88)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7470, 271, 7420])).
% 1.48/1.45 tff(7472,plain,
% 1.48/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s88, s89)) | node14(s88, s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s88, s89)) | node14(s88, s89))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7473,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s88, s89)) | node14(s88, s89))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7474,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s88, s89)) | node14(s88, s89)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7473, 7472])).
% 1.48/1.45 tff(7475,plain,
% 1.48/1.45 (node14(s88, s89)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7474, 7, 7431])).
% 1.48/1.45 tff(7476,plain,
% 1.48/1.45 (((~![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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, 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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7477,plain,
% 1.48/1.45 (((~m_main_v_state2(s88, c_c2)) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | m_main_v_state2(s89, c_n2)) <=> (m_main_v_state2(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7478,plain,
% 1.48/1.45 (((~![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(s88, c_c2)) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | m_main_v_state2(s89, 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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2))))),
% 1.48/1.45 inference(monotonicity,[status(thm)],[7477])).
% 1.48/1.45 tff(7479,plain,
% 1.48/1.45 (((~![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(s88, c_c2)) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | m_main_v_state2(s89, 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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2)))),
% 1.48/1.45 inference(transitivity,[status(thm)],[7478, 7476])).
% 1.48/1.45 tff(7480,plain,
% 1.48/1.45 ((~![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(s88, c_c2)) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | m_main_v_state2(s89, c_n2))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7481,plain,
% 1.48/1.45 ((~![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(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~node14(s88, s89)) | (~m_main_v_state2(s88, c_c2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7480, 7479])).
% 1.48/1.45 tff(7482,plain,
% 1.48/1.45 (m_main_v_state2(s89, c_n2) | node9(s88) | node8(s88) | node10(s88) | node11(s88) | node12(s88) | (~m_main_v_state2(s88, c_c2))),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7481, 726, 7475])).
% 1.48/1.45 tff(7483,plain,
% 1.48/1.45 (m_main_v_state2(s89, c_n2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7482, 7471, 7416, 7467, 7463, 7459, 7455])).
% 1.48/1.45 tff(7484,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_t2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7485,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_t2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7486,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_t2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7485, 7484])).
% 1.48/1.45 tff(7487,plain,
% 1.48/1.45 (~m_main_v_state2(s89, c_t2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7486, 77, 7483])).
% 1.48/1.45 tff(7488,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s89, c_t2) | (~node15(s89)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s89, c_t2) | (~node15(s89)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7489,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s89, c_t2) | (~node15(s89)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7490,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s89, c_t2) | (~node15(s89))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 1.48/1.45 tff(7491,plain,
% 1.48/1.45 (~node15(s89)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7490, 103, 7487])).
% 1.48/1.45 tff(7492,plain,
% 1.48/1.45 (succ(s89, s90) <=> succ(s89, s90)),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7493,axiom,(succ(s89, s90)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound90')).
% 1.48/1.45 tff(7494,plain,
% 1.48/1.45 (succ(s89, s90)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 1.48/1.45 tff(7495,plain,
% 1.48/1.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7496,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7497,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7496, 7495])).
% 1.48/1.45 tff(7498,plain,
% 1.48/1.45 (trans(s89, s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7497, 7494, 39])).
% 1.48/1.45 tff(7499,plain,
% 1.48/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s89, s90)) | node18(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s89, s90)) | node18(s89, s90))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7500,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s89, s90)) | node18(s89, s90))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7501,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s89, s90)) | node18(s89, s90)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7500, 7499])).
% 1.48/1.45 tff(7502,plain,
% 1.48/1.45 (node18(s89, s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7501, 125, 7498])).
% 1.48/1.45 tff(7503,plain,
% 1.48/1.45 (((~![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(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, 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(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7504,plain,
% 1.48/1.45 (((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node15(s89) | (~node18(s89, s90)) | m_main_v_turn(s90, c_1)) <=> (node15(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7505,plain,
% 1.48/1.45 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node15(s89) | (~node18(s89, s90)) | m_main_v_turn(s90, 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(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1)))),
% 1.48/1.45 inference(monotonicity,[status(thm)],[7504])).
% 1.48/1.45 tff(7506,plain,
% 1.48/1.45 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node15(s89) | (~node18(s89, s90)) | m_main_v_turn(s90, 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(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1))),
% 1.48/1.45 inference(transitivity,[status(thm)],[7505, 7503])).
% 1.48/1.45 tff(7507,plain,
% 1.48/1.45 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node15(s89) | (~node18(s89, s90)) | m_main_v_turn(s90, c_1))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7508,plain,
% 1.48/1.45 ((~![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(s89) | (~node18(s89, s90)) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 1.48/1.45 tff(7509,plain,
% 1.48/1.45 (node15(s89) | (~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_turn(s90, c_1)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7508, 992, 7502])).
% 1.48/1.45 tff(7510,plain,
% 1.48/1.45 (m_main_v_turn(s90, c_1)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7509, 7491, 7483, 7447])).
% 1.48/1.45 tff(7511,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s90, c_1)) | (~m_main_v_turn(s90, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s90, c_1)) | (~m_main_v_turn(s90, c_2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7512,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s90, c_1)) | (~m_main_v_turn(s90, c_2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7513,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s90, c_1)) | (~m_main_v_turn(s90, c_2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7512, 7511])).
% 1.48/1.45 tff(7514,plain,
% 1.48/1.45 (~m_main_v_turn(s90, c_2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7513, 156, 7510])).
% 1.48/1.45 tff(7515,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s90, c_2) | (~node12(s90)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s90, c_2) | (~node12(s90)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7516,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s90, c_2) | (~node12(s90)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7517,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s90, c_2) | (~node12(s90))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7516, 7515])).
% 1.48/1.45 tff(7518,plain,
% 1.48/1.45 (~node12(s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7517, 184, 7514])).
% 1.48/1.45 tff(7519,plain,
% 1.48/1.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s89, s90)) | node14(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s89, s90)) | node14(s89, s90))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7520,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s89, s90)) | node14(s89, s90))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7521,plain,
% 1.48/1.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s89, s90)) | node14(s89, s90)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7520, 7519])).
% 1.48/1.45 tff(7522,plain,
% 1.48/1.45 (node14(s89, s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7521, 7, 7498])).
% 1.48/1.45 tff(7523,plain,
% 1.48/1.45 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, 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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, c_t2))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7524,plain,
% 1.48/1.45 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, c_t2))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7525,plain,
% 1.48/1.45 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | (~node14(s89, s90)) | m_main_v_state2(s90, c_t2)),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7524, 7523])).
% 1.48/1.45 tff(7526,plain,
% 1.48/1.45 ((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state2(s90, c_t2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7525, 922, 7522])).
% 1.48/1.45 tff(7527,plain,
% 1.48/1.45 (m_main_v_state2(s90, c_t2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7526, 7447, 7483])).
% 1.48/1.45 tff(7528,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s90, c_n2)) | (~m_main_v_state2(s90, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s90, c_n2)) | (~m_main_v_state2(s90, c_t2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7529,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s90, c_n2)) | (~m_main_v_state2(s90, c_t2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7530,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s90, c_n2)) | (~m_main_v_state2(s90, c_t2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7529, 7528])).
% 1.48/1.45 tff(7531,plain,
% 1.48/1.45 (~m_main_v_state2(s90, c_n2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7530, 77, 7527])).
% 1.48/1.45 tff(7532,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s90, c_n2) | (~node8(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s90, c_n2) | (~node8(s90)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7533,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s90, c_n2) | (~node8(s90)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7534,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s90, c_n2) | (~node8(s90))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7533, 7532])).
% 1.48/1.45 tff(7535,plain,
% 1.48/1.45 (~node8(s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7534, 271, 7531])).
% 1.48/1.45 tff(7536,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s90, c_n2) | (~node9(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s90, c_n2) | (~node9(s90)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7537,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s90, c_n2) | (~node9(s90)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7538,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s90, c_n2) | (~node9(s90))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7537, 7536])).
% 1.48/1.45 tff(7539,plain,
% 1.48/1.45 (~node9(s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7538, 88, 7531])).
% 1.48/1.45 tff(7540,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s90, c_n2) | (~node10(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s90, c_n2) | (~node10(s90)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7541,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s90, c_n2) | (~node10(s90)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7542,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s90, c_n2) | (~node10(s90))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7541, 7540])).
% 1.48/1.45 tff(7543,plain,
% 1.48/1.45 (~node10(s90)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7542, 249, 7531])).
% 1.48/1.45 tff(7544,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s90, c_t2)) | (~m_main_v_state2(s90, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s90, c_t2)) | (~m_main_v_state2(s90, c_c2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7545,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s90, c_t2)) | (~m_main_v_state2(s90, c_c2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7546,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s90, c_t2)) | (~m_main_v_state2(s90, c_c2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 1.48/1.45 tff(7547,plain,
% 1.48/1.45 (~m_main_v_state2(s90, c_c2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7546, 260, 7527])).
% 1.48/1.45 tff(7548,plain,
% 1.48/1.45 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_c2)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7549,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_c2)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7550,plain,
% 1.48/1.45 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s89, c_n2)) | (~m_main_v_state2(s89, c_c2))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7549, 7548])).
% 1.48/1.45 tff(7551,plain,
% 1.48/1.45 (~m_main_v_state2(s89, c_c2)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7550, 697, 7483])).
% 1.48/1.45 tff(7552,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s89, c_c2) | (~node3(s89)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s89, c_c2) | (~node3(s89)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7553,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s89, c_c2) | (~node3(s89)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7554,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s89, c_c2) | (~node3(s89))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7553, 7552])).
% 1.48/1.45 tff(7555,plain,
% 1.48/1.45 (~node3(s89)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7554, 399, 7551])).
% 1.48/1.45 tff(7556,plain,
% 1.48/1.45 (((~![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(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89)))) <=> ((~![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(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7557,plain,
% 1.48/1.45 (((~node6(s88, s89)) | m_main_v_state1(s88, c_n1) | (~m_main_v_state1(s89, c_n1))) <=> (m_main_v_state1(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7558,plain,
% 1.48/1.45 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s88, s89)) | m_main_v_state1(s88, c_n1) | (~m_main_v_state1(s89, 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(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89))))),
% 1.48/1.45 inference(monotonicity,[status(thm)],[7557])).
% 1.48/1.45 tff(7559,plain,
% 1.48/1.45 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s88, s89)) | m_main_v_state1(s88, c_n1) | (~m_main_v_state1(s89, 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(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89)))),
% 1.48/1.45 inference(transitivity,[status(thm)],[7558, 7556])).
% 1.48/1.45 tff(7560,plain,
% 1.48/1.45 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s88, s89)) | m_main_v_state1(s88, c_n1) | (~m_main_v_state1(s89, c_n1)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7561,plain,
% 1.48/1.45 ((~![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(s88, c_n1) | (~m_main_v_state1(s89, c_n1)) | (~node6(s88, s89))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7560, 7559])).
% 1.48/1.45 tff(7562,plain,
% 1.48/1.45 (~m_main_v_state1(s89, c_n1)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7561, 835, 7355, 7440])).
% 1.48/1.45 tff(7563,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s89, c_n1) | (~node2(s89)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s89, c_n1) | (~node2(s89)))),
% 1.48/1.45 inference(rewrite,[status(thm)],[])).
% 1.48/1.45 tff(7564,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s89, c_n1) | (~node2(s89)))),
% 1.48/1.45 inference(quant_inst,[status(thm)],[])).
% 1.48/1.45 tff(7565,plain,
% 1.48/1.45 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s89, c_n1) | (~node2(s89))),
% 1.48/1.45 inference(modus_ponens,[status(thm)],[7564, 7563])).
% 1.48/1.45 tff(7566,plain,
% 1.48/1.45 (~node2(s89)),
% 1.48/1.45 inference(unit_resolution,[status(thm)],[7565, 787, 7562])).
% 1.48/1.45 tff(7567,plain,
% 1.48/1.45 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s89, c_t2) | (~node1(s89)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s89, c_t2) | (~node1(s89)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7568,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s89, c_t2) | (~node1(s89)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7569,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s89, c_t2) | (~node1(s89))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7568, 7567])).
% 1.48/1.46 tff(7570,plain,
% 1.48/1.46 (~node1(s89)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7569, 195, 7487])).
% 1.48/1.46 tff(7571,plain,
% 1.48/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s89, s90)) | node7(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s89, s90)) | node7(s89, s90))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7572,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s89, s90)) | node7(s89, s90))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7573,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s89, s90)) | node7(s89, s90)),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7572, 7571])).
% 1.48/1.46 tff(7574,plain,
% 1.48/1.46 (node7(s89, s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7573, 206, 7498])).
% 1.48/1.46 tff(7575,plain,
% 1.48/1.46 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)))) <=> ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7576,plain,
% 1.48/1.46 (((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)) | m_main_v_state1(s90, c_c1)) <=> ((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7577,plain,
% 1.48/1.46 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)) | m_main_v_state1(s90, 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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90))))),
% 1.48/1.46 inference(monotonicity,[status(thm)],[7576])).
% 1.48/1.46 tff(7578,plain,
% 1.48/1.46 (((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)) | m_main_v_state1(s90, 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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)))),
% 1.48/1.46 inference(transitivity,[status(thm)],[7577, 7575])).
% 1.48/1.46 tff(7579,plain,
% 1.48/1.46 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90)) | m_main_v_state1(s90, c_c1))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7580,plain,
% 1.48/1.46 ((~![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(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89) | (~node7(s89, s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7579, 7578])).
% 1.48/1.46 tff(7581,plain,
% 1.48/1.46 ((~m_main_v_state1(s89, c_t1)) | (~m_main_v_state2(s89, c_n2)) | m_main_v_state1(s90, c_c1) | node1(s89) | node2(s89) | node3(s89)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7580, 892, 7574])).
% 1.48/1.46 tff(7582,plain,
% 1.48/1.46 (m_main_v_state1(s90, c_c1)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7581, 7570, 7483, 7447, 7566, 7555])).
% 1.48/1.46 tff(7583,plain,
% 1.48/1.46 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s90, c_n1)) | (~m_main_v_state1(s90, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s90, c_n1)) | (~m_main_v_state1(s90, c_c1)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7584,plain,
% 1.48/1.46 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s90, c_n1)) | (~m_main_v_state1(s90, c_c1)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7585,plain,
% 1.48/1.46 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s90, c_n1)) | (~m_main_v_state1(s90, c_c1))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7584, 7583])).
% 1.48/1.46 tff(7586,plain,
% 1.48/1.46 (~m_main_v_state1(s90, c_n1)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7585, 454, 7582])).
% 1.48/1.46 tff(7587,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s90, c_n1) | (~node11(s90)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s90, c_n1) | (~node11(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7588,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s90, c_n1) | (~node11(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7589,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s90, c_n1) | (~node11(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7588, 7587])).
% 1.48/1.46 tff(7590,plain,
% 1.48/1.46 (~node11(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7589, 238, 7586])).
% 1.48/1.46 tff(7591,plain,
% 1.48/1.46 (succ(s90, s91) <=> succ(s90, s91)),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7592,axiom,(succ(s90, s91)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound91')).
% 1.48/1.46 tff(7593,plain,
% 1.48/1.46 (succ(s90, s91)),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7592, 7591])).
% 1.48/1.46 tff(7594,plain,
% 1.48/1.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7595,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7596,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91)),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 1.48/1.46 tff(7597,plain,
% 1.48/1.46 (trans(s90, s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7596, 7593, 39])).
% 1.48/1.46 tff(7598,plain,
% 1.48/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s90, s91)) | node14(s90, s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s90, s91)) | node14(s90, s91))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7599,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s90, s91)) | node14(s90, s91))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7600,plain,
% 1.48/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s90, s91)) | node14(s90, s91)),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7599, 7598])).
% 1.48/1.46 tff(7601,plain,
% 1.48/1.46 (node14(s90, s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7600, 7, 7597])).
% 1.48/1.46 tff(7602,plain,
% 1.48/1.46 (((~![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(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91)))) <=> ((~![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(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7603,plain,
% 1.48/1.46 ((~![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(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7604,plain,
% 1.48/1.46 ((~![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(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91) | (~node14(s90, s91))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7603, 7602])).
% 1.48/1.46 tff(7605,plain,
% 1.48/1.46 (m_main_v_state2(s90, c_c2) | node9(s90) | node8(s90) | node10(s90) | node11(s90) | node12(s90) | node13(s90, s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7604, 296, 7601])).
% 1.48/1.46 tff(7606,plain,
% 1.48/1.46 (node13(s90, s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7605, 7590, 7547, 7543, 7539, 7535, 7518])).
% 1.48/1.46 tff(7607,plain,
% 1.48/1.46 (((~![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(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91)))) <=> ((~![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(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7608,plain,
% 1.48/1.46 (((~node13(s90, s91)) | m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, c_n2))) <=> (m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7609,plain,
% 1.48/1.46 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s90, s91)) | m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, 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(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91))))),
% 1.48/1.46 inference(monotonicity,[status(thm)],[7608])).
% 1.48/1.46 tff(7610,plain,
% 1.48/1.46 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s90, s91)) | m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, 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(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91)))),
% 1.48/1.46 inference(transitivity,[status(thm)],[7609, 7607])).
% 1.48/1.46 tff(7611,plain,
% 1.48/1.46 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s90, s91)) | m_main_v_state2(s90, c_n2) | (~m_main_v_state2(s91, c_n2)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7612,plain,
% 1.48/1.46 ((~![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(s90, c_n2) | (~m_main_v_state2(s91, c_n2)) | (~node13(s90, s91))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7611, 7610])).
% 1.48/1.46 tff(7613,plain,
% 1.48/1.46 (~m_main_v_state2(s91, c_n2)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7612, 311, 7531, 7606])).
% 1.48/1.46 tff(7614,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s91, c_n2) | (~node9(s91)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s91, c_n2) | (~node9(s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7615,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s91, c_n2) | (~node9(s91)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7616,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s91, c_n2) | (~node9(s91))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 1.48/1.46 tff(7617,plain,
% 1.48/1.46 (~node9(s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7616, 88, 7613])).
% 1.48/1.46 tff(7618,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s91, c_n2) | (~node10(s91)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s91, c_n2) | (~node10(s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7619,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s91, c_n2) | (~node10(s91)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7620,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s91, c_n2) | (~node10(s91))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7619, 7618])).
% 1.48/1.46 tff(7621,plain,
% 1.48/1.46 (~node10(s91)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7620, 249, 7613])).
% 1.48/1.46 tff(7622,plain,
% 1.48/1.46 (((~![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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91)))) <=> ((~![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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7623,plain,
% 1.48/1.46 (((~node13(s90, s91)) | (~m_main_v_state2(s90, c_t2)) | m_main_v_state2(s91, c_t2)) <=> ((~m_main_v_state2(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7624,plain,
% 1.48/1.46 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s90, s91)) | (~m_main_v_state2(s90, c_t2)) | m_main_v_state2(s91, 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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91))))),
% 1.48/1.46 inference(monotonicity,[status(thm)],[7623])).
% 1.48/1.46 tff(7625,plain,
% 1.48/1.46 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s90, s91)) | (~m_main_v_state2(s90, c_t2)) | m_main_v_state2(s91, 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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91)))),
% 1.48/1.46 inference(transitivity,[status(thm)],[7624, 7622])).
% 1.48/1.46 tff(7626,plain,
% 1.48/1.46 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s90, s91)) | (~m_main_v_state2(s90, c_t2)) | m_main_v_state2(s91, c_t2))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7627,plain,
% 1.48/1.46 ((~![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(s90, c_t2)) | m_main_v_state2(s91, c_t2) | (~node13(s90, s91))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7626, 7625])).
% 1.48/1.46 tff(7628,plain,
% 1.48/1.46 (m_main_v_state2(s91, c_t2)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7627, 518, 7527, 7606])).
% 1.48/1.46 tff(7629,plain,
% 1.48/1.46 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s90, c_t1)) | (~m_main_v_state1(s90, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s90, c_t1)) | (~m_main_v_state1(s90, c_c1)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7630,plain,
% 1.48/1.46 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s90, c_t1)) | (~m_main_v_state1(s90, c_c1)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7631,plain,
% 1.48/1.46 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s90, c_t1)) | (~m_main_v_state1(s90, c_c1))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7630, 7629])).
% 1.48/1.46 tff(7632,plain,
% 1.48/1.46 (~m_main_v_state1(s90, c_t1)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7631, 539, 7582])).
% 1.48/1.46 tff(7633,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s90, c_t1) | (~node5(s90)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s90, c_t1) | (~node5(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7634,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s90, c_t1) | (~node5(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7635,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s90, c_t1) | (~node5(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7634, 7633])).
% 1.48/1.46 tff(7636,plain,
% 1.48/1.46 (~node5(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7635, 550, 7632])).
% 1.48/1.46 tff(7637,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s90, c_n2) | (~node4(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s90, c_n2) | (~node4(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7638,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s90, c_n2) | (~node4(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7639,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s90, c_n2) | (~node4(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7638, 7637])).
% 1.48/1.46 tff(7640,plain,
% 1.48/1.46 (~node4(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7639, 388, 7531])).
% 1.48/1.46 tff(7641,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s90, c_c2) | (~node3(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s90, c_c2) | (~node3(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7642,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s90, c_c2) | (~node3(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7643,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s90, c_c2) | (~node3(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.48/1.46 tff(7644,plain,
% 1.48/1.46 (~node3(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7643, 399, 7547])).
% 1.48/1.46 tff(7645,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s90, c_n2) | (~node2(s90)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s90, c_n2) | (~node2(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7646,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s90, c_n2) | (~node2(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7647,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s90, c_n2) | (~node2(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7646, 7645])).
% 1.48/1.46 tff(7648,plain,
% 1.48/1.46 (~node2(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7647, 410, 7531])).
% 1.48/1.46 tff(7649,plain,
% 1.48/1.46 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s90, c_n1) | (~node1(s90)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s90, c_n1) | (~node1(s90)))),
% 1.48/1.46 inference(rewrite,[status(thm)],[])).
% 1.48/1.46 tff(7650,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s90, c_n1) | (~node1(s90)))),
% 1.48/1.46 inference(quant_inst,[status(thm)],[])).
% 1.48/1.46 tff(7651,plain,
% 1.48/1.46 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s90, c_n1) | (~node1(s90))),
% 1.48/1.46 inference(modus_ponens,[status(thm)],[7650, 7649])).
% 1.48/1.46 tff(7652,plain,
% 1.48/1.46 (~node1(s90)),
% 1.48/1.46 inference(unit_resolution,[status(thm)],[7651, 421, 7586])).
% 1.48/1.46 tff(7653,plain,
% 1.48/1.46 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s90, s91)) | node7(s90, s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s90, s91)) | node7(s90, s91))),
% 1.55/1.46 inference(rewrite,[status(thm)],[])).
% 1.55/1.46 tff(7654,plain,
% 1.55/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s90, s91)) | node7(s90, s91))),
% 1.55/1.46 inference(quant_inst,[status(thm)],[])).
% 1.55/1.46 tff(7655,plain,
% 1.55/1.46 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s90, s91)) | node7(s90, s91)),
% 1.55/1.46 inference(modus_ponens,[status(thm)],[7654, 7653])).
% 1.55/1.46 tff(7656,plain,
% 1.55/1.46 (node7(s90, s91)),
% 1.55/1.46 inference(unit_resolution,[status(thm)],[7655, 206, 7597])).
% 1.55/1.46 tff(7657,plain,
% 1.55/1.46 (((~![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(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)))) <=> ((~![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(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)))),
% 1.55/1.46 inference(rewrite,[status(thm)],[])).
% 1.55/1.46 tff(7658,plain,
% 1.55/1.46 (((~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)) | m_main_v_state1(s91, c_n1)) <=> (m_main_v_state1(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)))),
% 1.55/1.46 inference(rewrite,[status(thm)],[])).
% 1.55/1.46 tff(7659,plain,
% 1.55/1.46 (((~![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(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)) | m_main_v_state1(s91, 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(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91))))),
% 1.55/1.46 inference(monotonicity,[status(thm)],[7658])).
% 1.55/1.46 tff(7660,plain,
% 1.55/1.46 (((~![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(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)) | m_main_v_state1(s91, 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(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)))),
% 1.55/1.46 inference(transitivity,[status(thm)],[7659, 7657])).
% 1.55/1.46 tff(7661,plain,
% 1.55/1.46 ((~![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(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91)) | m_main_v_state1(s91, c_n1))),
% 1.55/1.46 inference(quant_inst,[status(thm)],[])).
% 1.55/1.46 tff(7662,plain,
% 1.55/1.46 ((~![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(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90) | (~node7(s90, s91))),
% 1.55/1.46 inference(modus_ponens,[status(thm)],[7661, 7660])).
% 1.55/1.46 tff(7663,plain,
% 1.55/1.46 (m_main_v_state1(s91, c_n1) | (~m_main_v_state1(s90, c_c1)) | node1(s90) | node2(s90) | node3(s90) | node4(s90) | node5(s90)),
% 1.55/1.46 inference(unit_resolution,[status(thm)],[7662, 584, 7656])).
% 1.55/1.46 tff(7664,plain,
% 1.55/1.46 (m_main_v_state1(s91, c_n1)),
% 1.55/1.46 inference(unit_resolution,[status(thm)],[7663, 7652, 7582, 7648, 7644, 7640, 7636])).
% 1.55/1.46 tff(7665,plain,
% 1.55/1.46 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s91, c_n2) | (~node8(s91)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s91, c_n2) | (~node8(s91)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7666,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s91, c_n2) | (~node8(s91)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7667,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s91, c_n2) | (~node8(s91))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 1.55/1.47 tff(7668,plain,
% 1.55/1.47 (~node8(s91)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7667, 271, 7613])).
% 1.55/1.47 tff(7669,plain,
% 1.55/1.47 (succ(s91, s92) <=> succ(s91, s92)),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7670,axiom,(succ(s91, s92)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound92')).
% 1.55/1.47 tff(7671,plain,
% 1.55/1.47 (succ(s91, s92)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7670, 7669])).
% 1.55/1.47 tff(7672,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7673,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7674,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7673, 7672])).
% 1.55/1.47 tff(7675,plain,
% 1.55/1.47 (trans(s91, s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7674, 7671, 39])).
% 1.55/1.47 tff(7676,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s91, s92)) | node14(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s91, s92)) | node14(s91, s92))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7677,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s91, s92)) | node14(s91, s92))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7678,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s91, s92)) | node14(s91, s92)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7677, 7676])).
% 1.55/1.47 tff(7679,plain,
% 1.55/1.47 (node14(s91, s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7678, 7, 7675])).
% 1.55/1.47 tff(7680,plain,
% 1.55/1.47 (((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | node9(s91) | node8(s91) | node10(s91) | (~node14(s91, s92)) | m_main_v_state2(s92, 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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | node9(s91) | node8(s91) | node10(s91) | (~node14(s91, s92)) | m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7681,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | node9(s91) | node8(s91) | node10(s91) | (~node14(s91, s92)) | m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7682,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | node9(s91) | node8(s91) | node10(s91) | (~node14(s91, s92)) | m_main_v_state2(s92, c_c2)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 1.55/1.47 tff(7683,plain,
% 1.55/1.47 ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | node9(s91) | node8(s91) | node10(s91) | m_main_v_state2(s92, c_c2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7682, 617, 7679])).
% 1.55/1.47 tff(7684,plain,
% 1.55/1.47 (m_main_v_state2(s92, c_c2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7683, 7668, 7664, 7628, 7621, 7617])).
% 1.55/1.47 tff(7685,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s92, c_t2)) | (~m_main_v_state2(s92, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s92, c_t2)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7686,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s92, c_t2)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7687,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s92, c_t2)) | (~m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7686, 7685])).
% 1.55/1.47 tff(7688,plain,
% 1.55/1.47 (~m_main_v_state2(s92, c_t2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7687, 260, 7684])).
% 1.55/1.47 tff(7689,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s92, c_t2) | (~node12(s92)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s92, c_t2) | (~node12(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7690,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s92, c_t2) | (~node12(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7691,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s92, c_t2) | (~node12(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7690, 7689])).
% 1.55/1.47 tff(7692,plain,
% 1.55/1.47 (~node12(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7691, 633, 7688])).
% 1.55/1.47 tff(7693,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s91, s92)) | node7(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s91, s92)) | node7(s91, s92))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7694,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s91, s92)) | node7(s91, s92))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7695,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s91, s92)) | node7(s91, s92)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7694, 7693])).
% 1.55/1.47 tff(7696,plain,
% 1.55/1.47 (node7(s91, s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7695, 206, 7675])).
% 1.55/1.47 tff(7697,plain,
% 1.55/1.47 (((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, 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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, c_t1))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7698,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, c_t1))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7699,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node7(s91, s92)) | m_main_v_state1(s92, c_t1)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7698, 7697])).
% 1.55/1.47 tff(7700,plain,
% 1.55/1.47 ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | m_main_v_state1(s92, c_t1)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7699, 651, 7696])).
% 1.55/1.47 tff(7701,plain,
% 1.55/1.47 (m_main_v_state1(s92, c_t1)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7700, 7628, 7664])).
% 1.55/1.47 tff(7702,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s92, c_n1)) | (~m_main_v_state1(s92, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s92, c_n1)) | (~m_main_v_state1(s92, c_t1)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7703,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s92, c_n1)) | (~m_main_v_state1(s92, c_t1)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7704,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s92, c_n1)) | (~m_main_v_state1(s92, c_t1))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7703, 7702])).
% 1.55/1.47 tff(7705,plain,
% 1.55/1.47 (~m_main_v_state1(s92, c_n1)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7704, 17, 7701])).
% 1.55/1.47 tff(7706,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s92, c_n1) | (~node11(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s92, c_n1) | (~node11(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7707,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s92, c_n1) | (~node11(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7708,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s92, c_n1) | (~node11(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 1.55/1.47 tff(7709,plain,
% 1.55/1.47 (~node11(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7708, 238, 7705])).
% 1.55/1.47 tff(7710,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s92, c_t1)) | (~m_main_v_state1(s92, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s92, c_t1)) | (~m_main_v_state1(s92, c_c1)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7711,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s92, c_t1)) | (~m_main_v_state1(s92, c_c1)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7712,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s92, c_t1)) | (~m_main_v_state1(s92, c_c1))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7711, 7710])).
% 1.55/1.47 tff(7713,plain,
% 1.55/1.47 (~m_main_v_state1(s92, c_c1)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7712, 539, 7701])).
% 1.55/1.47 tff(7714,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s92, c_c1) | (~node10(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s92, c_c1) | (~node10(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7715,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s92, c_c1) | (~node10(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7716,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s92, c_c1) | (~node10(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7715, 7714])).
% 1.55/1.47 tff(7717,plain,
% 1.55/1.47 (~node10(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7716, 675, 7713])).
% 1.55/1.47 tff(7718,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s92, c_n1) | (~node9(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s92, c_n1) | (~node9(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7719,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s92, c_n1) | (~node9(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7720,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s92, c_n1) | (~node9(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7719, 7718])).
% 1.55/1.47 tff(7721,plain,
% 1.55/1.47 (~node9(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7720, 686, 7705])).
% 1.55/1.47 tff(7722,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s92, c_n2)) | (~m_main_v_state2(s92, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s92, c_n2)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7723,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s92, c_n2)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7724,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s92, c_n2)) | (~m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7723, 7722])).
% 1.55/1.47 tff(7725,plain,
% 1.55/1.47 (~m_main_v_state2(s92, c_n2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7724, 697, 7684])).
% 1.55/1.47 tff(7726,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s92, c_n2) | (~node8(s92)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s92, c_n2) | (~node8(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7727,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s92, c_n2) | (~node8(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7728,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s92, c_n2) | (~node8(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7727, 7726])).
% 1.55/1.47 tff(7729,plain,
% 1.55/1.47 (~node8(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7728, 271, 7725])).
% 1.55/1.47 tff(7730,plain,
% 1.55/1.47 (succ(s92, s93) <=> succ(s92, s93)),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7731,axiom,(succ(s92, s93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound93')).
% 1.55/1.47 tff(7732,plain,
% 1.55/1.47 (succ(s92, s93)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7731, 7730])).
% 1.55/1.47 tff(7733,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7734,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7735,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7734, 7733])).
% 1.55/1.47 tff(7736,plain,
% 1.55/1.47 (trans(s92, s93)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7735, 7732, 39])).
% 1.55/1.47 tff(7737,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s92, s93)) | node14(s92, s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s92, s93)) | node14(s92, s93))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7738,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s92, s93)) | node14(s92, s93))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7739,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s92, s93)) | node14(s92, s93)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7738, 7737])).
% 1.55/1.47 tff(7740,plain,
% 1.55/1.47 (node14(s92, s93)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7739, 7, 7736])).
% 1.55/1.47 tff(7741,plain,
% 1.55/1.47 (((~![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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, 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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7742,plain,
% 1.55/1.47 (((~m_main_v_state2(s92, c_c2)) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | m_main_v_state2(s93, c_n2)) <=> (m_main_v_state2(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7743,plain,
% 1.55/1.47 (((~![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(s92, c_c2)) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | m_main_v_state2(s93, 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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2))))),
% 1.55/1.47 inference(monotonicity,[status(thm)],[7742])).
% 1.55/1.47 tff(7744,plain,
% 1.55/1.47 (((~![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(s92, c_c2)) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | m_main_v_state2(s93, 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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2)))),
% 1.55/1.47 inference(transitivity,[status(thm)],[7743, 7741])).
% 1.55/1.47 tff(7745,plain,
% 1.55/1.47 ((~![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(s92, c_c2)) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | m_main_v_state2(s93, c_n2))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7746,plain,
% 1.55/1.47 ((~![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(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~node14(s92, s93)) | (~m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7745, 7744])).
% 1.55/1.47 tff(7747,plain,
% 1.55/1.47 (m_main_v_state2(s93, c_n2) | node9(s92) | node8(s92) | node10(s92) | node11(s92) | node12(s92) | (~m_main_v_state2(s92, c_c2))),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7746, 726, 7740])).
% 1.55/1.47 tff(7748,plain,
% 1.55/1.47 (m_main_v_state2(s93, c_n2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7747, 7729, 7684, 7721, 7717, 7709, 7692])).
% 1.55/1.47 tff(7749,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_c2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7750,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_c2)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7751,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_c2))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7750, 7749])).
% 1.55/1.47 tff(7752,plain,
% 1.55/1.47 (~m_main_v_state2(s93, c_c2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7751, 697, 7748])).
% 1.55/1.47 tff(7753,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s93, c_c2) | (~node3(s93)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s93, c_c2) | (~node3(s93)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7754,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s93, c_c2) | (~node3(s93)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7755,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s93, c_c2) | (~node3(s93))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 1.55/1.47 tff(7756,plain,
% 1.55/1.47 (~node3(s93)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7755, 399, 7752])).
% 1.55/1.47 tff(7757,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s92, c_n1) | (~node1(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s92, c_n1) | (~node1(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7758,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s92, c_n1) | (~node1(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7759,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s92, c_n1) | (~node1(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7758, 7757])).
% 1.55/1.47 tff(7760,plain,
% 1.55/1.47 (~node1(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7759, 421, 7705])).
% 1.55/1.47 tff(7761,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s91, s92)) | node18(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s91, s92)) | node18(s91, s92))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7762,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s91, s92)) | node18(s91, s92))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7763,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s91, s92)) | node18(s91, s92)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7762, 7761])).
% 1.55/1.47 tff(7764,plain,
% 1.55/1.47 (node18(s91, s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7763, 125, 7675])).
% 1.55/1.47 tff(7765,plain,
% 1.55/1.47 (((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, 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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, c_2))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7766,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, c_2))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7767,plain,
% 1.55/1.47 ((~![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(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | (~node18(s91, s92)) | m_main_v_turn(s92, c_2)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 1.55/1.47 tff(7768,plain,
% 1.55/1.47 ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state2(s91, c_t2)) | m_main_v_turn(s92, c_2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7767, 760, 7764])).
% 1.55/1.47 tff(7769,plain,
% 1.55/1.47 (m_main_v_turn(s92, c_2)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7768, 7628, 7664])).
% 1.55/1.47 tff(7770,plain,
% 1.55/1.47 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s92, c_1)) | (~m_main_v_turn(s92, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s92, c_1)) | (~m_main_v_turn(s92, c_2)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7771,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s92, c_1)) | (~m_main_v_turn(s92, c_2)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7772,plain,
% 1.55/1.47 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s92, c_1)) | (~m_main_v_turn(s92, c_2))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7771, 7770])).
% 1.55/1.47 tff(7773,plain,
% 1.55/1.47 (~m_main_v_turn(s92, c_1)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7772, 156, 7769])).
% 1.55/1.47 tff(7774,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s92, c_1) | (~node5(s92)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s92, c_1) | (~node5(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7775,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s92, c_1) | (~node5(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7776,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s92, c_1) | (~node5(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7775, 7774])).
% 1.55/1.47 tff(7777,plain,
% 1.55/1.47 (~node5(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7776, 776, 7773])).
% 1.55/1.47 tff(7778,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s92, c_n1) | (~node2(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s92, c_n1) | (~node2(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7779,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s92, c_n1) | (~node2(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7780,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s92, c_n1) | (~node2(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7779, 7778])).
% 1.55/1.47 tff(7781,plain,
% 1.55/1.47 (~node2(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7780, 787, 7705])).
% 1.55/1.47 tff(7782,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s92, c_n1) | (~node3(s92)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s92, c_n1) | (~node3(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7783,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s92, c_n1) | (~node3(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7784,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s92, c_n1) | (~node3(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7783, 7782])).
% 1.55/1.47 tff(7785,plain,
% 1.55/1.47 (~node3(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7784, 798, 7705])).
% 1.55/1.47 tff(7786,plain,
% 1.55/1.47 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s92, c_n2) | (~node4(s92)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s92, c_n2) | (~node4(s92)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7787,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s92, c_n2) | (~node4(s92)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7788,plain,
% 1.55/1.47 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s92, c_n2) | (~node4(s92))),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7787, 7786])).
% 1.55/1.47 tff(7789,plain,
% 1.55/1.47 (~node4(s92)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7788, 388, 7725])).
% 1.55/1.47 tff(7790,plain,
% 1.55/1.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s92, s93)) | node7(s92, s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s92, s93)) | node7(s92, s93))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7791,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s92, s93)) | node7(s92, s93))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.47 tff(7792,plain,
% 1.55/1.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s92, s93)) | node7(s92, s93)),
% 1.55/1.47 inference(modus_ponens,[status(thm)],[7791, 7790])).
% 1.55/1.47 tff(7793,plain,
% 1.55/1.47 (node7(s92, s93)),
% 1.55/1.47 inference(unit_resolution,[status(thm)],[7792, 206, 7736])).
% 1.55/1.47 tff(7794,plain,
% 1.55/1.47 (((~![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(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93)))) <=> ((~![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(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93)))),
% 1.55/1.47 inference(rewrite,[status(thm)],[])).
% 1.55/1.47 tff(7795,plain,
% 1.55/1.47 ((~![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(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93)))),
% 1.55/1.47 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7796,plain,
% 1.55/1.48 ((~![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(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93) | (~node7(s92, s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7795, 7794])).
% 1.55/1.48 tff(7797,plain,
% 1.55/1.48 (m_main_v_state1(s92, c_c1) | node1(s92) | node2(s92) | node3(s92) | node4(s92) | node5(s92) | node6(s92, s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7796, 820, 7793])).
% 1.55/1.48 tff(7798,plain,
% 1.55/1.48 (node6(s92, s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7797, 7789, 7713, 7785, 7781, 7777, 7760])).
% 1.55/1.48 tff(7799,plain,
% 1.55/1.48 (((~![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(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93)))) <=> ((~![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(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7800,plain,
% 1.55/1.48 (((~node6(s92, s93)) | m_main_v_state1(s92, c_n1) | (~m_main_v_state1(s93, c_n1))) <=> (m_main_v_state1(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7801,plain,
% 1.55/1.48 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s92, s93)) | m_main_v_state1(s92, c_n1) | (~m_main_v_state1(s93, 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(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93))))),
% 1.55/1.48 inference(monotonicity,[status(thm)],[7800])).
% 1.55/1.48 tff(7802,plain,
% 1.55/1.48 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s92, s93)) | m_main_v_state1(s92, c_n1) | (~m_main_v_state1(s93, 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(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93)))),
% 1.55/1.48 inference(transitivity,[status(thm)],[7801, 7799])).
% 1.55/1.48 tff(7803,plain,
% 1.55/1.48 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s92, s93)) | m_main_v_state1(s92, c_n1) | (~m_main_v_state1(s93, c_n1)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7804,plain,
% 1.55/1.48 ((~![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(s92, c_n1) | (~m_main_v_state1(s93, c_n1)) | (~node6(s92, s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7803, 7802])).
% 1.55/1.48 tff(7805,plain,
% 1.55/1.48 (~m_main_v_state1(s93, c_n1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7804, 835, 7705, 7798])).
% 1.55/1.48 tff(7806,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s93, c_n1) | (~node2(s93)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s93, c_n1) | (~node2(s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7807,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s93, c_n1) | (~node2(s93)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7808,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s93, c_n1) | (~node2(s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7807, 7806])).
% 1.55/1.48 tff(7809,plain,
% 1.55/1.48 (~node2(s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7808, 787, 7805])).
% 1.55/1.48 tff(7810,plain,
% 1.55/1.48 (((~![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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93)))) <=> ((~![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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7811,plain,
% 1.55/1.48 (((~node6(s92, s93)) | (~m_main_v_state1(s92, c_t1)) | m_main_v_state1(s93, c_t1)) <=> ((~m_main_v_state1(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7812,plain,
% 1.55/1.48 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s92, s93)) | (~m_main_v_state1(s92, c_t1)) | m_main_v_state1(s93, 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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93))))),
% 1.55/1.48 inference(monotonicity,[status(thm)],[7811])).
% 1.55/1.48 tff(7813,plain,
% 1.55/1.48 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s92, s93)) | (~m_main_v_state1(s92, c_t1)) | m_main_v_state1(s93, 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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93)))),
% 1.55/1.48 inference(transitivity,[status(thm)],[7812, 7810])).
% 1.55/1.48 tff(7814,plain,
% 1.55/1.48 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s92, s93)) | (~m_main_v_state1(s92, c_t1)) | m_main_v_state1(s93, c_t1))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7815,plain,
% 1.55/1.48 ((~![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(s92, c_t1)) | m_main_v_state1(s93, c_t1) | (~node6(s92, s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7814, 7813])).
% 1.55/1.48 tff(7816,plain,
% 1.55/1.48 (m_main_v_state1(s93, c_t1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7815, 856, 7701, 7798])).
% 1.55/1.48 tff(7817,plain,
% 1.55/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_t2)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7818,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_t2)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7819,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s93, c_n2)) | (~m_main_v_state2(s93, c_t2))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7818, 7817])).
% 1.55/1.48 tff(7820,plain,
% 1.55/1.48 (~m_main_v_state2(s93, c_t2)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7819, 77, 7748])).
% 1.55/1.48 tff(7821,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s93, c_t2) | (~node1(s93)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s93, c_t2) | (~node1(s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7822,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s93, c_t2) | (~node1(s93)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7823,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s93, c_t2) | (~node1(s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7822, 7821])).
% 1.55/1.48 tff(7824,plain,
% 1.55/1.48 (~node1(s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7823, 195, 7820])).
% 1.55/1.48 tff(7825,plain,
% 1.55/1.48 (succ(s93, s94) <=> succ(s93, s94)),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7826,axiom,(succ(s93, s94)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound94')).
% 1.55/1.48 tff(7827,plain,
% 1.55/1.48 (succ(s93, s94)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7826, 7825])).
% 1.55/1.48 tff(7828,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7829,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7830,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7829, 7828])).
% 1.55/1.48 tff(7831,plain,
% 1.55/1.48 (trans(s93, s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7830, 7827, 39])).
% 1.55/1.48 tff(7832,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s93, s94)) | node7(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s93, s94)) | node7(s93, s94))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7833,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s93, s94)) | node7(s93, s94))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7834,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s93, s94)) | node7(s93, s94)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7833, 7832])).
% 1.55/1.48 tff(7835,plain,
% 1.55/1.48 (node7(s93, s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7834, 206, 7831])).
% 1.55/1.48 tff(7836,plain,
% 1.55/1.48 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)))) <=> ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7837,plain,
% 1.55/1.48 (((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)) | m_main_v_state1(s94, c_c1)) <=> ((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7838,plain,
% 1.55/1.48 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)) | m_main_v_state1(s94, 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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94))))),
% 1.55/1.48 inference(monotonicity,[status(thm)],[7837])).
% 1.55/1.48 tff(7839,plain,
% 1.55/1.48 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)) | m_main_v_state1(s94, 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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)))),
% 1.55/1.48 inference(transitivity,[status(thm)],[7838, 7836])).
% 1.55/1.48 tff(7840,plain,
% 1.55/1.48 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94)) | m_main_v_state1(s94, c_c1))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7841,plain,
% 1.55/1.48 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93) | (~node7(s93, s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7840, 7839])).
% 1.55/1.48 tff(7842,plain,
% 1.55/1.48 ((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state1(s94, c_c1) | node1(s93) | node2(s93) | node3(s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7841, 892, 7835])).
% 1.55/1.48 tff(7843,plain,
% 1.55/1.48 (m_main_v_state1(s94, c_c1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7842, 7824, 7748, 7816, 7809, 7756])).
% 1.55/1.48 tff(7844,plain,
% 1.55/1.48 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s94, c_t1)) | (~m_main_v_state1(s94, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s94, c_t1)) | (~m_main_v_state1(s94, c_c1)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7845,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s94, c_t1)) | (~m_main_v_state1(s94, c_c1)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7846,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s94, c_t1)) | (~m_main_v_state1(s94, c_c1))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7845, 7844])).
% 1.55/1.48 tff(7847,plain,
% 1.55/1.48 (~m_main_v_state1(s94, c_t1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7846, 539, 7843])).
% 1.55/1.48 tff(7848,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s94, c_t1) | (~node5(s94)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s94, c_t1) | (~node5(s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7849,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s94, c_t1) | (~node5(s94)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7850,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s94, c_t1) | (~node5(s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7849, 7848])).
% 1.55/1.48 tff(7851,plain,
% 1.55/1.48 (~node5(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7850, 550, 7847])).
% 1.55/1.48 tff(7852,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s93, s94)) | node14(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s93, s94)) | node14(s93, s94))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7853,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s93, s94)) | node14(s93, s94))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7854,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s93, s94)) | node14(s93, s94)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7853, 7852])).
% 1.55/1.48 tff(7855,plain,
% 1.55/1.48 (node14(s93, s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7854, 7, 7831])).
% 1.55/1.48 tff(7856,plain,
% 1.55/1.48 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | (~node14(s93, s94)) | m_main_v_state2(s94, 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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | (~node14(s93, s94)) | m_main_v_state2(s94, c_t2))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7857,plain,
% 1.55/1.48 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | (~node14(s93, s94)) | m_main_v_state2(s94, c_t2))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7858,plain,
% 1.55/1.48 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | (~node14(s93, s94)) | m_main_v_state2(s94, c_t2)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7857, 7856])).
% 1.55/1.48 tff(7859,plain,
% 1.55/1.48 ((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_state2(s94, c_t2)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7858, 922, 7855])).
% 1.55/1.48 tff(7860,plain,
% 1.55/1.48 (m_main_v_state2(s94, c_t2)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7859, 7816, 7748])).
% 1.55/1.48 tff(7861,plain,
% 1.55/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s94, c_n2)) | (~m_main_v_state2(s94, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s94, c_n2)) | (~m_main_v_state2(s94, c_t2)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7862,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s94, c_n2)) | (~m_main_v_state2(s94, c_t2)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7863,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s94, c_n2)) | (~m_main_v_state2(s94, c_t2))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7862, 7861])).
% 1.55/1.48 tff(7864,plain,
% 1.55/1.48 (~m_main_v_state2(s94, c_n2)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7863, 77, 7860])).
% 1.55/1.48 tff(7865,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s94, c_n2) | (~node4(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s94, c_n2) | (~node4(s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7866,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s94, c_n2) | (~node4(s94)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7867,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s94, c_n2) | (~node4(s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7866, 7865])).
% 1.55/1.48 tff(7868,plain,
% 1.55/1.48 (~node4(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7867, 388, 7864])).
% 1.55/1.48 tff(7869,plain,
% 1.55/1.48 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s94, c_t2)) | (~m_main_v_state2(s94, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s94, c_t2)) | (~m_main_v_state2(s94, c_c2)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7870,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s94, c_t2)) | (~m_main_v_state2(s94, c_c2)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7871,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s94, c_t2)) | (~m_main_v_state2(s94, c_c2))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7870, 7869])).
% 1.55/1.48 tff(7872,plain,
% 1.55/1.48 (~m_main_v_state2(s94, c_c2)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7871, 260, 7860])).
% 1.55/1.48 tff(7873,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s94, c_c2) | (~node3(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s94, c_c2) | (~node3(s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7874,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s94, c_c2) | (~node3(s94)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7875,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s94, c_c2) | (~node3(s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7874, 7873])).
% 1.55/1.48 tff(7876,plain,
% 1.55/1.48 (~node3(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7875, 399, 7872])).
% 1.55/1.48 tff(7877,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s94, c_n2) | (~node2(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s94, c_n2) | (~node2(s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7878,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s94, c_n2) | (~node2(s94)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7879,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s94, c_n2) | (~node2(s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7878, 7877])).
% 1.55/1.48 tff(7880,plain,
% 1.55/1.48 (~node2(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7879, 410, 7864])).
% 1.55/1.48 tff(7881,plain,
% 1.55/1.48 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s94, c_n1)) | (~m_main_v_state1(s94, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s94, c_n1)) | (~m_main_v_state1(s94, c_c1)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7882,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s94, c_n1)) | (~m_main_v_state1(s94, c_c1)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7883,plain,
% 1.55/1.48 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s94, c_n1)) | (~m_main_v_state1(s94, c_c1))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 1.55/1.48 tff(7884,plain,
% 1.55/1.48 (~m_main_v_state1(s94, c_n1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7883, 454, 7843])).
% 1.55/1.48 tff(7885,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s94, c_n1) | (~node1(s94)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s94, c_n1) | (~node1(s94)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7886,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s94, c_n1) | (~node1(s94)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7887,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s94, c_n1) | (~node1(s94))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7886, 7885])).
% 1.55/1.48 tff(7888,plain,
% 1.55/1.48 (~node1(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7887, 421, 7884])).
% 1.55/1.48 tff(7889,plain,
% 1.55/1.48 (succ(s94, s95) <=> succ(s94, s95)),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7890,axiom,(succ(s94, s95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound95')).
% 1.55/1.48 tff(7891,plain,
% 1.55/1.48 (succ(s94, s95)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7890, 7889])).
% 1.55/1.48 tff(7892,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7893,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7894,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7893, 7892])).
% 1.55/1.48 tff(7895,plain,
% 1.55/1.48 (trans(s94, s95)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7894, 7891, 39])).
% 1.55/1.48 tff(7896,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s94, s95)) | node7(s94, s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s94, s95)) | node7(s94, s95))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7897,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s94, s95)) | node7(s94, s95))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7898,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s94, s95)) | node7(s94, s95)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7897, 7896])).
% 1.55/1.48 tff(7899,plain,
% 1.55/1.48 (node7(s94, s95)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7898, 206, 7895])).
% 1.55/1.48 tff(7900,plain,
% 1.55/1.48 (((~![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(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)))) <=> ((~![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(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7901,plain,
% 1.55/1.48 (((~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)) | m_main_v_state1(s95, c_n1)) <=> (m_main_v_state1(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7902,plain,
% 1.55/1.48 (((~![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(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)) | m_main_v_state1(s95, 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(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95))))),
% 1.55/1.48 inference(monotonicity,[status(thm)],[7901])).
% 1.55/1.48 tff(7903,plain,
% 1.55/1.48 (((~![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(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)) | m_main_v_state1(s95, 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(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)))),
% 1.55/1.48 inference(transitivity,[status(thm)],[7902, 7900])).
% 1.55/1.48 tff(7904,plain,
% 1.55/1.48 ((~![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(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95)) | m_main_v_state1(s95, c_n1))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7905,plain,
% 1.55/1.48 ((~![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(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94) | (~node7(s94, s95))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7904, 7903])).
% 1.55/1.48 tff(7906,plain,
% 1.55/1.48 (m_main_v_state1(s95, c_n1) | (~m_main_v_state1(s94, c_c1)) | node1(s94) | node2(s94) | node3(s94) | node4(s94) | node5(s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7905, 584, 7899])).
% 1.55/1.48 tff(7907,plain,
% 1.55/1.48 (m_main_v_state1(s95, c_n1)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7906, 7888, 7843, 7880, 7876, 7868, 7851])).
% 1.55/1.48 tff(7908,plain,
% 1.55/1.48 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s93, c_t2) | (~node15(s93)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s93, c_t2) | (~node15(s93)))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7909,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s93, c_t2) | (~node15(s93)))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7910,plain,
% 1.55/1.48 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s93, c_t2) | (~node15(s93))),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7909, 7908])).
% 1.55/1.48 tff(7911,plain,
% 1.55/1.48 (~node15(s93)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7910, 103, 7820])).
% 1.55/1.48 tff(7912,plain,
% 1.55/1.48 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s93, s94)) | node18(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s93, s94)) | node18(s93, s94))),
% 1.55/1.48 inference(rewrite,[status(thm)],[])).
% 1.55/1.48 tff(7913,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s93, s94)) | node18(s93, s94))),
% 1.55/1.48 inference(quant_inst,[status(thm)],[])).
% 1.55/1.48 tff(7914,plain,
% 1.55/1.48 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s93, s94)) | node18(s93, s94)),
% 1.55/1.48 inference(modus_ponens,[status(thm)],[7913, 7912])).
% 1.55/1.48 tff(7915,plain,
% 1.55/1.48 (node18(s93, s94)),
% 1.55/1.48 inference(unit_resolution,[status(thm)],[7914, 125, 7831])).
% 1.55/1.48 tff(7916,plain,
% 1.55/1.49 (((~![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(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, 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(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7917,plain,
% 1.55/1.49 (((~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node15(s93) | (~node18(s93, s94)) | m_main_v_turn(s94, c_1)) <=> (node15(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7918,plain,
% 1.55/1.49 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node15(s93) | (~node18(s93, s94)) | m_main_v_turn(s94, 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(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1)))),
% 1.55/1.49 inference(monotonicity,[status(thm)],[7917])).
% 1.55/1.49 tff(7919,plain,
% 1.55/1.49 (((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node15(s93) | (~node18(s93, s94)) | m_main_v_turn(s94, 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(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1))),
% 1.55/1.49 inference(transitivity,[status(thm)],[7918, 7916])).
% 1.55/1.49 tff(7920,plain,
% 1.55/1.49 ((~![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(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | node15(s93) | (~node18(s93, s94)) | m_main_v_turn(s94, c_1))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7921,plain,
% 1.55/1.49 ((~![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(s93) | (~node18(s93, s94)) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7920, 7919])).
% 1.55/1.49 tff(7922,plain,
% 1.55/1.49 (node15(s93) | (~m_main_v_state1(s93, c_t1)) | (~m_main_v_state2(s93, c_n2)) | m_main_v_turn(s94, c_1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7921, 992, 7915])).
% 1.55/1.49 tff(7923,plain,
% 1.55/1.49 (m_main_v_turn(s94, c_1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7922, 7911, 7748, 7816])).
% 1.55/1.49 tff(7924,plain,
% 1.55/1.49 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s94, c_1)) | (~m_main_v_turn(s94, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s94, c_1)) | (~m_main_v_turn(s94, c_2)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7925,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s94, c_1)) | (~m_main_v_turn(s94, c_2)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7926,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s94, c_1)) | (~m_main_v_turn(s94, c_2))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7925, 7924])).
% 1.55/1.49 tff(7927,plain,
% 1.55/1.49 (~m_main_v_turn(s94, c_2)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7926, 156, 7923])).
% 1.55/1.49 tff(7928,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s94, c_2) | (~node12(s94)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s94, c_2) | (~node12(s94)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7929,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s94, c_2) | (~node12(s94)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7930,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s94, c_2) | (~node12(s94))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7929, 7928])).
% 1.55/1.49 tff(7931,plain,
% 1.55/1.49 (~node12(s94)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7930, 184, 7927])).
% 1.55/1.49 tff(7932,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s94, c_n2) | (~node8(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s94, c_n2) | (~node8(s94)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7933,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s94, c_n2) | (~node8(s94)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7934,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s94, c_n2) | (~node8(s94))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7933, 7932])).
% 1.55/1.49 tff(7935,plain,
% 1.55/1.49 (~node8(s94)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7934, 271, 7864])).
% 1.55/1.49 tff(7936,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s94, c_n2) | (~node9(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s94, c_n2) | (~node9(s94)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7937,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s94, c_n2) | (~node9(s94)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7938,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s94, c_n2) | (~node9(s94))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7937, 7936])).
% 1.55/1.49 tff(7939,plain,
% 1.55/1.49 (~node9(s94)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7938, 88, 7864])).
% 1.55/1.49 tff(7940,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s94, c_n2) | (~node10(s94)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s94, c_n2) | (~node10(s94)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7941,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s94, c_n2) | (~node10(s94)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7942,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s94, c_n2) | (~node10(s94))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7941, 7940])).
% 1.55/1.49 tff(7943,plain,
% 1.55/1.49 (~node10(s94)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7942, 249, 7864])).
% 1.55/1.49 tff(7944,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s94, c_n1) | (~node11(s94)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s94, c_n1) | (~node11(s94)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7945,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s94, c_n1) | (~node11(s94)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7946,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s94, c_n1) | (~node11(s94))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7945, 7944])).
% 1.55/1.49 tff(7947,plain,
% 1.55/1.49 (~node11(s94)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7946, 238, 7884])).
% 1.55/1.49 tff(7948,plain,
% 1.55/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s94, s95)) | node14(s94, s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s94, s95)) | node14(s94, s95))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7949,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s94, s95)) | node14(s94, s95))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7950,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s94, s95)) | node14(s94, s95)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7949, 7948])).
% 1.55/1.49 tff(7951,plain,
% 1.55/1.49 (node14(s94, s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7950, 7, 7895])).
% 1.55/1.49 tff(7952,plain,
% 1.55/1.49 (((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95)))) <=> ((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7953,plain,
% 1.55/1.49 ((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7954,plain,
% 1.55/1.49 ((~![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(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95) | (~node14(s94, s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7953, 7952])).
% 1.55/1.49 tff(7955,plain,
% 1.55/1.49 (m_main_v_state2(s94, c_c2) | node9(s94) | node8(s94) | node10(s94) | node11(s94) | node12(s94) | node13(s94, s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7954, 296, 7951])).
% 1.55/1.49 tff(7956,plain,
% 1.55/1.49 (node13(s94, s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7955, 7947, 7872, 7943, 7939, 7935, 7931])).
% 1.55/1.49 tff(7957,plain,
% 1.55/1.49 (((~![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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95)))) <=> ((~![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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7958,plain,
% 1.55/1.49 (((~node13(s94, s95)) | (~m_main_v_state2(s94, c_t2)) | m_main_v_state2(s95, c_t2)) <=> ((~m_main_v_state2(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7959,plain,
% 1.55/1.49 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s94, s95)) | (~m_main_v_state2(s94, c_t2)) | m_main_v_state2(s95, 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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95))))),
% 1.55/1.49 inference(monotonicity,[status(thm)],[7958])).
% 1.55/1.49 tff(7960,plain,
% 1.55/1.49 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s94, s95)) | (~m_main_v_state2(s94, c_t2)) | m_main_v_state2(s95, 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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95)))),
% 1.55/1.49 inference(transitivity,[status(thm)],[7959, 7957])).
% 1.55/1.49 tff(7961,plain,
% 1.55/1.49 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s94, s95)) | (~m_main_v_state2(s94, c_t2)) | m_main_v_state2(s95, c_t2))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7962,plain,
% 1.55/1.49 ((~![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(s94, c_t2)) | m_main_v_state2(s95, c_t2) | (~node13(s94, s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 1.55/1.49 tff(7963,plain,
% 1.55/1.49 (m_main_v_state2(s95, c_t2)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7962, 518, 7860, 7956])).
% 1.55/1.49 tff(7964,plain,
% 1.55/1.49 (succ(s95, s96) <=> succ(s95, s96)),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7965,axiom,(succ(s95, s96)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound96')).
% 1.55/1.49 tff(7966,plain,
% 1.55/1.49 (succ(s95, s96)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7965, 7964])).
% 1.55/1.49 tff(7967,plain,
% 1.55/1.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7968,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7969,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7968, 7967])).
% 1.55/1.49 tff(7970,plain,
% 1.55/1.49 (trans(s95, s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7969, 7966, 39])).
% 1.55/1.49 tff(7971,plain,
% 1.55/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s95, s96)) | node7(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s95, s96)) | node7(s95, s96))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7972,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s95, s96)) | node7(s95, s96))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7973,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s95, s96)) | node7(s95, s96)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7972, 7971])).
% 1.55/1.49 tff(7974,plain,
% 1.55/1.49 (node7(s95, s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7973, 206, 7970])).
% 1.55/1.49 tff(7975,plain,
% 1.55/1.49 (((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node7(s95, s96)) | m_main_v_state1(s96, 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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node7(s95, s96)) | m_main_v_state1(s96, c_t1))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7976,plain,
% 1.55/1.49 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node7(s95, s96)) | m_main_v_state1(s96, c_t1))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7977,plain,
% 1.55/1.49 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node7(s95, s96)) | m_main_v_state1(s96, c_t1)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7976, 7975])).
% 1.55/1.49 tff(7978,plain,
% 1.55/1.49 ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | m_main_v_state1(s96, c_t1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7977, 651, 7974])).
% 1.55/1.49 tff(7979,plain,
% 1.55/1.49 (m_main_v_state1(s96, c_t1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7978, 7963, 7907])).
% 1.55/1.49 tff(7980,plain,
% 1.55/1.49 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s96, c_n1)) | (~m_main_v_state1(s96, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s96, c_n1)) | (~m_main_v_state1(s96, c_t1)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7981,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s96, c_n1)) | (~m_main_v_state1(s96, c_t1)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7982,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s96, c_n1)) | (~m_main_v_state1(s96, c_t1))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7981, 7980])).
% 1.55/1.49 tff(7983,plain,
% 1.55/1.49 (~m_main_v_state1(s96, c_n1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7982, 17, 7979])).
% 1.55/1.49 tff(7984,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s96, c_n1) | (~node1(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s96, c_n1) | (~node1(s96)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7985,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s96, c_n1) | (~node1(s96)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7986,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s96, c_n1) | (~node1(s96))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7985, 7984])).
% 1.55/1.49 tff(7987,plain,
% 1.55/1.49 (~node1(s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7986, 421, 7983])).
% 1.55/1.49 tff(7988,plain,
% 1.55/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s95, s96)) | node18(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s95, s96)) | node18(s95, s96))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7989,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s95, s96)) | node18(s95, s96))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7990,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s95, s96)) | node18(s95, s96)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7989, 7988])).
% 1.55/1.49 tff(7991,plain,
% 1.55/1.49 (node18(s95, s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7990, 125, 7970])).
% 1.55/1.49 tff(7992,plain,
% 1.55/1.49 (((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node18(s95, s96)) | m_main_v_turn(s96, 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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node18(s95, s96)) | m_main_v_turn(s96, c_2))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7993,plain,
% 1.55/1.49 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node18(s95, s96)) | m_main_v_turn(s96, c_2))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7994,plain,
% 1.55/1.49 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | (~node18(s95, s96)) | m_main_v_turn(s96, c_2)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7993, 7992])).
% 1.55/1.49 tff(7995,plain,
% 1.55/1.49 ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | m_main_v_turn(s96, c_2)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7994, 760, 7991])).
% 1.55/1.49 tff(7996,plain,
% 1.55/1.49 (m_main_v_turn(s96, c_2)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7995, 7963, 7907])).
% 1.55/1.49 tff(7997,plain,
% 1.55/1.49 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s96, c_1)) | (~m_main_v_turn(s96, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s96, c_1)) | (~m_main_v_turn(s96, c_2)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(7998,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s96, c_1)) | (~m_main_v_turn(s96, c_2)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(7999,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s96, c_1)) | (~m_main_v_turn(s96, c_2))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[7998, 7997])).
% 1.55/1.49 tff(8000,plain,
% 1.55/1.49 (~m_main_v_turn(s96, c_1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[7999, 156, 7996])).
% 1.55/1.49 tff(8001,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s96, c_1) | (~node5(s96)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s96, c_1) | (~node5(s96)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8002,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s96, c_1) | (~node5(s96)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8003,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s96, c_1) | (~node5(s96))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8002, 8001])).
% 1.55/1.49 tff(8004,plain,
% 1.55/1.49 (~node5(s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8003, 776, 8000])).
% 1.55/1.49 tff(8005,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s96, c_n1) | (~node2(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s96, c_n1) | (~node2(s96)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8006,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s96, c_n1) | (~node2(s96)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8007,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s96, c_n1) | (~node2(s96))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8006, 8005])).
% 1.55/1.49 tff(8008,plain,
% 1.55/1.49 (~node2(s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8007, 787, 7983])).
% 1.55/1.49 tff(8009,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s96, c_n1) | (~node3(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s96, c_n1) | (~node3(s96)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8010,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s96, c_n1) | (~node3(s96)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8011,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s96, c_n1) | (~node3(s96))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 1.55/1.49 tff(8012,plain,
% 1.55/1.49 (~node3(s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8011, 798, 7983])).
% 1.55/1.49 tff(8013,plain,
% 1.55/1.49 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s96, c_t1)) | (~m_main_v_state1(s96, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s96, c_t1)) | (~m_main_v_state1(s96, c_c1)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8014,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s96, c_t1)) | (~m_main_v_state1(s96, c_c1)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8015,plain,
% 1.55/1.49 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s96, c_t1)) | (~m_main_v_state1(s96, c_c1))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 1.55/1.49 tff(8016,plain,
% 1.55/1.49 (~m_main_v_state1(s96, c_c1)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8015, 539, 7979])).
% 1.55/1.49 tff(8017,plain,
% 1.55/1.49 (((~![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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95)))) <=> ((~![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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8018,plain,
% 1.55/1.49 (((~node13(s94, s95)) | m_main_v_state2(s94, c_n2) | (~m_main_v_state2(s95, c_n2))) <=> (m_main_v_state2(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8019,plain,
% 1.55/1.49 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s94, s95)) | m_main_v_state2(s94, c_n2) | (~m_main_v_state2(s95, 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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95))))),
% 1.55/1.49 inference(monotonicity,[status(thm)],[8018])).
% 1.55/1.49 tff(8020,plain,
% 1.55/1.49 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s94, s95)) | m_main_v_state2(s94, c_n2) | (~m_main_v_state2(s95, 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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95)))),
% 1.55/1.49 inference(transitivity,[status(thm)],[8019, 8017])).
% 1.55/1.49 tff(8021,plain,
% 1.55/1.49 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s94, s95)) | m_main_v_state2(s94, c_n2) | (~m_main_v_state2(s95, c_n2)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8022,plain,
% 1.55/1.49 ((~![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(s94, c_n2) | (~m_main_v_state2(s95, c_n2)) | (~node13(s94, s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8021, 8020])).
% 1.55/1.49 tff(8023,plain,
% 1.55/1.49 (~m_main_v_state2(s95, c_n2)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8022, 311, 7864, 7956])).
% 1.55/1.49 tff(8024,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s95, c_n2) | (~node9(s95)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s95, c_n2) | (~node9(s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8025,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s95, c_n2) | (~node9(s95)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8026,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s95, c_n2) | (~node9(s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8025, 8024])).
% 1.55/1.49 tff(8027,plain,
% 1.55/1.49 (~node9(s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8026, 88, 8023])).
% 1.55/1.49 tff(8028,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s95, c_n2) | (~node10(s95)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s95, c_n2) | (~node10(s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8029,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s95, c_n2) | (~node10(s95)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8030,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s95, c_n2) | (~node10(s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8029, 8028])).
% 1.55/1.49 tff(8031,plain,
% 1.55/1.49 (~node10(s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8030, 249, 8023])).
% 1.55/1.49 tff(8032,plain,
% 1.55/1.49 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s95, c_n2) | (~node8(s95)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s95, c_n2) | (~node8(s95)))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8033,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s95, c_n2) | (~node8(s95)))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8034,plain,
% 1.55/1.49 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s95, c_n2) | (~node8(s95))),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8033, 8032])).
% 1.55/1.49 tff(8035,plain,
% 1.55/1.49 (~node8(s95)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8034, 271, 8023])).
% 1.55/1.49 tff(8036,plain,
% 1.55/1.49 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s95, s96)) | node14(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s95, s96)) | node14(s95, s96))),
% 1.55/1.49 inference(rewrite,[status(thm)],[])).
% 1.55/1.49 tff(8037,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s95, s96)) | node14(s95, s96))),
% 1.55/1.49 inference(quant_inst,[status(thm)],[])).
% 1.55/1.49 tff(8038,plain,
% 1.55/1.49 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s95, s96)) | node14(s95, s96)),
% 1.55/1.49 inference(modus_ponens,[status(thm)],[8037, 8036])).
% 1.55/1.49 tff(8039,plain,
% 1.55/1.49 (node14(s95, s96)),
% 1.55/1.49 inference(unit_resolution,[status(thm)],[8038, 7, 7970])).
% 1.55/1.49 tff(8040,plain,
% 1.55/1.49 (((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | node9(s95) | node8(s95) | node10(s95) | (~node14(s95, s96)) | m_main_v_state2(s96, 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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | node9(s95) | node8(s95) | node10(s95) | (~node14(s95, s96)) | m_main_v_state2(s96, c_c2))),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8041,plain,
% 1.55/1.50 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | node9(s95) | node8(s95) | node10(s95) | (~node14(s95, s96)) | m_main_v_state2(s96, c_c2))),
% 1.55/1.50 inference(quant_inst,[status(thm)],[])).
% 1.55/1.50 tff(8042,plain,
% 1.55/1.50 ((~![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(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | node9(s95) | node8(s95) | node10(s95) | (~node14(s95, s96)) | m_main_v_state2(s96, c_c2)),
% 1.55/1.50 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 1.55/1.50 tff(8043,plain,
% 1.55/1.50 ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state2(s95, c_t2)) | node9(s95) | node8(s95) | node10(s95) | m_main_v_state2(s96, c_c2)),
% 1.55/1.50 inference(unit_resolution,[status(thm)],[8042, 617, 8039])).
% 1.55/1.50 tff(8044,plain,
% 1.55/1.50 (m_main_v_state2(s96, c_c2)),
% 1.55/1.50 inference(unit_resolution,[status(thm)],[8043, 8035, 7907, 7963, 8031, 8027])).
% 1.55/1.50 tff(8045,plain,
% 1.55/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s96, c_n2)) | (~m_main_v_state2(s96, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s96, c_n2)) | (~m_main_v_state2(s96, c_c2)))),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8046,plain,
% 1.55/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s96, c_n2)) | (~m_main_v_state2(s96, c_c2)))),
% 1.55/1.50 inference(quant_inst,[status(thm)],[])).
% 1.55/1.50 tff(8047,plain,
% 1.55/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s96, c_n2)) | (~m_main_v_state2(s96, c_c2))),
% 1.55/1.50 inference(modus_ponens,[status(thm)],[8046, 8045])).
% 1.55/1.50 tff(8048,plain,
% 1.55/1.50 (~m_main_v_state2(s96, c_n2)),
% 1.55/1.50 inference(unit_resolution,[status(thm)],[8047, 697, 8044])).
% 1.55/1.50 tff(8049,plain,
% 1.55/1.50 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s96, c_n2) | (~node4(s96)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s96, c_n2) | (~node4(s96)))),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8050,plain,
% 1.55/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s96, c_n2) | (~node4(s96)))),
% 1.55/1.50 inference(quant_inst,[status(thm)],[])).
% 1.55/1.50 tff(8051,plain,
% 1.55/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s96, c_n2) | (~node4(s96))),
% 1.55/1.50 inference(modus_ponens,[status(thm)],[8050, 8049])).
% 1.55/1.50 tff(8052,plain,
% 1.55/1.50 (~node4(s96)),
% 1.55/1.50 inference(unit_resolution,[status(thm)],[8051, 388, 8048])).
% 1.55/1.50 tff(8053,plain,
% 1.55/1.50 (succ(s96, s97) <=> succ(s96, s97)),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8054,axiom,(succ(s96, s97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound97')).
% 1.55/1.50 tff(8055,plain,
% 1.55/1.50 (succ(s96, s97)),
% 1.55/1.50 inference(modus_ponens,[status(thm)],[8054, 8053])).
% 1.55/1.50 tff(8056,plain,
% 1.55/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97))),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8057,plain,
% 1.55/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))),
% 1.55/1.50 inference(quant_inst,[status(thm)],[])).
% 1.55/1.50 tff(8058,plain,
% 1.55/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97)),
% 1.55/1.50 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 1.55/1.50 tff(8059,plain,
% 1.55/1.50 (trans(s96, s97)),
% 1.55/1.50 inference(unit_resolution,[status(thm)],[8058, 8055, 39])).
% 1.55/1.50 tff(8060,plain,
% 1.55/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s96, s97)) | node7(s96, s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s96, s97)) | node7(s96, s97))),
% 1.55/1.50 inference(rewrite,[status(thm)],[])).
% 1.55/1.50 tff(8061,plain,
% 1.55/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s96, s97)) | node7(s96, s97))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8062,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s96, s97)) | node7(s96, s97)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8061, 8060])).
% 1.58/1.50 tff(8063,plain,
% 1.58/1.50 (node7(s96, s97)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8062, 206, 8059])).
% 1.58/1.50 tff(8064,plain,
% 1.58/1.50 (((~![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(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97) | (~node7(s96, s97)))) <=> ((~![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(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97) | (~node7(s96, s97)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8065,plain,
% 1.58/1.50 ((~![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(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97) | (~node7(s96, s97)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8066,plain,
% 1.58/1.50 ((~![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(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97) | (~node7(s96, s97))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8065, 8064])).
% 1.58/1.50 tff(8067,plain,
% 1.58/1.50 (m_main_v_state1(s96, c_c1) | node1(s96) | node2(s96) | node3(s96) | node4(s96) | node5(s96) | node6(s96, s97)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8066, 820, 8063])).
% 1.58/1.50 tff(8068,plain,
% 1.58/1.50 (node6(s96, s97)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8067, 8052, 8016, 8012, 8008, 8004, 7987])).
% 1.58/1.50 tff(8069,plain,
% 1.58/1.50 (((~![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(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97)))) <=> ((~![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(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8070,plain,
% 1.58/1.50 (((~node6(s96, s97)) | (~m_main_v_state1(s96, c_t1)) | m_main_v_state1(s97, c_t1)) <=> ((~m_main_v_state1(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8071,plain,
% 1.58/1.50 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s96, s97)) | (~m_main_v_state1(s96, c_t1)) | m_main_v_state1(s97, 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(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97))))),
% 1.58/1.50 inference(monotonicity,[status(thm)],[8070])).
% 1.58/1.50 tff(8072,plain,
% 1.58/1.50 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s96, s97)) | (~m_main_v_state1(s96, c_t1)) | m_main_v_state1(s97, 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(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97)))),
% 1.58/1.50 inference(transitivity,[status(thm)],[8071, 8069])).
% 1.58/1.50 tff(8073,plain,
% 1.58/1.50 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s96, s97)) | (~m_main_v_state1(s96, c_t1)) | m_main_v_state1(s97, c_t1))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8074,plain,
% 1.58/1.50 ((~![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(s96, c_t1)) | m_main_v_state1(s97, c_t1) | (~node6(s96, s97))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8073, 8072])).
% 1.58/1.50 tff(8075,plain,
% 1.58/1.50 (m_main_v_state1(s97, c_t1)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8074, 856, 7979, 8068])).
% 1.58/1.50 tff(8076,plain,
% 1.58/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s96, c_t2)) | (~m_main_v_state2(s96, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s96, c_t2)) | (~m_main_v_state2(s96, c_c2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8077,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s96, c_t2)) | (~m_main_v_state2(s96, c_c2)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8078,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s96, c_t2)) | (~m_main_v_state2(s96, c_c2))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8077, 8076])).
% 1.58/1.50 tff(8079,plain,
% 1.58/1.50 (~m_main_v_state2(s96, c_t2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8078, 260, 8044])).
% 1.58/1.50 tff(8080,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s96, c_t2) | (~node12(s96)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s96, c_t2) | (~node12(s96)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8081,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s96, c_t2) | (~node12(s96)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8082,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s96, c_t2) | (~node12(s96))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 1.58/1.50 tff(8083,plain,
% 1.58/1.50 (~node12(s96)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8082, 633, 8079])).
% 1.58/1.50 tff(8084,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s96, c_n1) | (~node11(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s96, c_n1) | (~node11(s96)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8085,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s96, c_n1) | (~node11(s96)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8086,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s96, c_n1) | (~node11(s96))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 1.58/1.50 tff(8087,plain,
% 1.58/1.50 (~node11(s96)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8086, 238, 7983])).
% 1.58/1.50 tff(8088,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s96, c_c1) | (~node10(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s96, c_c1) | (~node10(s96)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8089,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s96, c_c1) | (~node10(s96)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8090,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s96, c_c1) | (~node10(s96))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8089, 8088])).
% 1.58/1.50 tff(8091,plain,
% 1.58/1.50 (~node10(s96)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8090, 675, 8016])).
% 1.58/1.50 tff(8092,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s96, c_n1) | (~node9(s96)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s96, c_n1) | (~node9(s96)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8093,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s96, c_n1) | (~node9(s96)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8094,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s96, c_n1) | (~node9(s96))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 1.58/1.50 tff(8095,plain,
% 1.58/1.50 (~node9(s96)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8094, 686, 7983])).
% 1.58/1.50 tff(8096,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s96, c_n2) | (~node8(s96)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s96, c_n2) | (~node8(s96)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8097,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s96, c_n2) | (~node8(s96)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8098,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s96, c_n2) | (~node8(s96))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8097, 8096])).
% 1.58/1.50 tff(8099,plain,
% 1.58/1.50 (~node8(s96)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8098, 271, 8048])).
% 1.58/1.50 tff(8100,plain,
% 1.58/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s96, s97)) | node14(s96, s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s96, s97)) | node14(s96, s97))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8101,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s96, s97)) | node14(s96, s97))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8102,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s96, s97)) | node14(s96, s97)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8101, 8100])).
% 1.58/1.50 tff(8103,plain,
% 1.58/1.50 (node14(s96, s97)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8102, 7, 8059])).
% 1.58/1.50 tff(8104,plain,
% 1.58/1.50 (((~![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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, 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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8105,plain,
% 1.58/1.50 (((~m_main_v_state2(s96, c_c2)) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | m_main_v_state2(s97, c_n2)) <=> (m_main_v_state2(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8106,plain,
% 1.58/1.50 (((~![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(s96, c_c2)) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | m_main_v_state2(s97, 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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2))))),
% 1.58/1.50 inference(monotonicity,[status(thm)],[8105])).
% 1.58/1.50 tff(8107,plain,
% 1.58/1.50 (((~![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(s96, c_c2)) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | m_main_v_state2(s97, 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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2)))),
% 1.58/1.50 inference(transitivity,[status(thm)],[8106, 8104])).
% 1.58/1.50 tff(8108,plain,
% 1.58/1.50 ((~![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(s96, c_c2)) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | m_main_v_state2(s97, c_n2))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8109,plain,
% 1.58/1.50 ((~![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(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~node14(s96, s97)) | (~m_main_v_state2(s96, c_c2))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8108, 8107])).
% 1.58/1.50 tff(8110,plain,
% 1.58/1.50 (m_main_v_state2(s97, c_n2) | node9(s96) | node8(s96) | node10(s96) | node11(s96) | node12(s96) | (~m_main_v_state2(s96, c_c2))),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8109, 726, 8103])).
% 1.58/1.50 tff(8111,plain,
% 1.58/1.50 (m_main_v_state2(s97, c_n2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8110, 8099, 8044, 8095, 8091, 8087, 8083])).
% 1.58/1.50 tff(8112,plain,
% 1.58/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_t2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8113,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_t2)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8114,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_t2))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8113, 8112])).
% 1.58/1.50 tff(8115,plain,
% 1.58/1.50 (~m_main_v_state2(s97, c_t2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8114, 77, 8111])).
% 1.58/1.50 tff(8116,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s97, c_t2) | (~node15(s97)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s97, c_t2) | (~node15(s97)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8117,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s97, c_t2) | (~node15(s97)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8118,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s97, c_t2) | (~node15(s97))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8117, 8116])).
% 1.58/1.50 tff(8119,plain,
% 1.58/1.50 (~node15(s97)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8118, 103, 8115])).
% 1.58/1.50 tff(8120,plain,
% 1.58/1.50 (succ(s97, s98) <=> succ(s97, s98)),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8121,axiom,(succ(s97, s98)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound98')).
% 1.58/1.50 tff(8122,plain,
% 1.58/1.50 (succ(s97, s98)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8121, 8120])).
% 1.58/1.50 tff(8123,plain,
% 1.58/1.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8124,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8125,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8124, 8123])).
% 1.58/1.50 tff(8126,plain,
% 1.58/1.50 (trans(s97, s98)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8125, 8122, 39])).
% 1.58/1.50 tff(8127,plain,
% 1.58/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s97, s98)) | node18(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s97, s98)) | node18(s97, s98))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8128,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s97, s98)) | node18(s97, s98))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8129,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s97, s98)) | node18(s97, s98)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8128, 8127])).
% 1.58/1.50 tff(8130,plain,
% 1.58/1.50 (node18(s97, s98)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8129, 125, 8126])).
% 1.58/1.50 tff(8131,plain,
% 1.58/1.50 (((~![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(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, 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(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8132,plain,
% 1.58/1.50 (((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node15(s97) | (~node18(s97, s98)) | m_main_v_turn(s98, c_1)) <=> (node15(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8133,plain,
% 1.58/1.50 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node15(s97) | (~node18(s97, s98)) | m_main_v_turn(s98, 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(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1)))),
% 1.58/1.50 inference(monotonicity,[status(thm)],[8132])).
% 1.58/1.50 tff(8134,plain,
% 1.58/1.50 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node15(s97) | (~node18(s97, s98)) | m_main_v_turn(s98, 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(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1))),
% 1.58/1.50 inference(transitivity,[status(thm)],[8133, 8131])).
% 1.58/1.50 tff(8135,plain,
% 1.58/1.50 ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node15(s97) | (~node18(s97, s98)) | m_main_v_turn(s98, c_1))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8136,plain,
% 1.58/1.50 ((~![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(s97) | (~node18(s97, s98)) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8135, 8134])).
% 1.58/1.50 tff(8137,plain,
% 1.58/1.50 (node15(s97) | (~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_turn(s98, c_1)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8136, 992, 8130])).
% 1.58/1.50 tff(8138,plain,
% 1.58/1.50 (m_main_v_turn(s98, c_1)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8137, 8119, 8111, 8075])).
% 1.58/1.50 tff(8139,plain,
% 1.58/1.50 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s98, c_1)) | (~m_main_v_turn(s98, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s98, c_1)) | (~m_main_v_turn(s98, c_2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8140,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s98, c_1)) | (~m_main_v_turn(s98, c_2)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8141,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s98, c_1)) | (~m_main_v_turn(s98, c_2))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8140, 8139])).
% 1.58/1.50 tff(8142,plain,
% 1.58/1.50 (~m_main_v_turn(s98, c_2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8141, 156, 8138])).
% 1.58/1.50 tff(8143,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s98, c_2) | (~node12(s98)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s98, c_2) | (~node12(s98)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8144,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s98, c_2) | (~node12(s98)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8145,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s98, c_2) | (~node12(s98))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8144, 8143])).
% 1.58/1.50 tff(8146,plain,
% 1.58/1.50 (~node12(s98)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8145, 184, 8142])).
% 1.58/1.50 tff(8147,plain,
% 1.58/1.50 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s97, s98)) | node14(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s97, s98)) | node14(s97, s98))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8148,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s97, s98)) | node14(s97, s98))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8149,plain,
% 1.58/1.50 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s97, s98)) | node14(s97, s98)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8148, 8147])).
% 1.58/1.50 tff(8150,plain,
% 1.58/1.50 (node14(s97, s98)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8149, 7, 8126])).
% 1.58/1.50 tff(8151,plain,
% 1.58/1.50 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | (~node14(s97, s98)) | m_main_v_state2(s98, 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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | (~node14(s97, s98)) | m_main_v_state2(s98, c_t2))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8152,plain,
% 1.58/1.50 ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | (~node14(s97, s98)) | m_main_v_state2(s98, c_t2))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8153,plain,
% 1.58/1.50 ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | (~node14(s97, s98)) | m_main_v_state2(s98, c_t2)),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8152, 8151])).
% 1.58/1.50 tff(8154,plain,
% 1.58/1.50 ((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state2(s98, c_t2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8153, 922, 8150])).
% 1.58/1.50 tff(8155,plain,
% 1.58/1.50 (m_main_v_state2(s98, c_t2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8154, 8075, 8111])).
% 1.58/1.50 tff(8156,plain,
% 1.58/1.50 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s98, c_n2)) | (~m_main_v_state2(s98, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s98, c_n2)) | (~m_main_v_state2(s98, c_t2)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8157,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s98, c_n2)) | (~m_main_v_state2(s98, c_t2)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8158,plain,
% 1.58/1.50 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s98, c_n2)) | (~m_main_v_state2(s98, c_t2))),
% 1.58/1.50 inference(modus_ponens,[status(thm)],[8157, 8156])).
% 1.58/1.50 tff(8159,plain,
% 1.58/1.50 (~m_main_v_state2(s98, c_n2)),
% 1.58/1.50 inference(unit_resolution,[status(thm)],[8158, 77, 8155])).
% 1.58/1.50 tff(8160,plain,
% 1.58/1.50 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s98, c_n2) | (~node8(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s98, c_n2) | (~node8(s98)))),
% 1.58/1.50 inference(rewrite,[status(thm)],[])).
% 1.58/1.50 tff(8161,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s98, c_n2) | (~node8(s98)))),
% 1.58/1.50 inference(quant_inst,[status(thm)],[])).
% 1.58/1.50 tff(8162,plain,
% 1.58/1.50 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s98, c_n2) | (~node8(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8161, 8160])).
% 1.58/1.51 tff(8163,plain,
% 1.58/1.51 (~node8(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8162, 271, 8159])).
% 1.58/1.51 tff(8164,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s98, c_n2) | (~node9(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s98, c_n2) | (~node9(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8165,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s98, c_n2) | (~node9(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8166,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s98, c_n2) | (~node9(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8165, 8164])).
% 1.58/1.51 tff(8167,plain,
% 1.58/1.51 (~node9(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8166, 88, 8159])).
% 1.58/1.51 tff(8168,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s98, c_n2) | (~node10(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s98, c_n2) | (~node10(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8169,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s98, c_n2) | (~node10(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8170,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s98, c_n2) | (~node10(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 1.58/1.51 tff(8171,plain,
% 1.58/1.51 (~node10(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8170, 249, 8159])).
% 1.58/1.51 tff(8172,plain,
% 1.58/1.51 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s98, c_t2)) | (~m_main_v_state2(s98, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s98, c_t2)) | (~m_main_v_state2(s98, c_c2)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8173,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s98, c_t2)) | (~m_main_v_state2(s98, c_c2)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8174,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s98, c_t2)) | (~m_main_v_state2(s98, c_c2))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8173, 8172])).
% 1.58/1.51 tff(8175,plain,
% 1.58/1.51 (~m_main_v_state2(s98, c_c2)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8174, 260, 8155])).
% 1.58/1.51 tff(8176,plain,
% 1.58/1.51 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_c2)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8177,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_c2)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8178,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s97, c_n2)) | (~m_main_v_state2(s97, c_c2))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8177, 8176])).
% 1.58/1.51 tff(8179,plain,
% 1.58/1.51 (~m_main_v_state2(s97, c_c2)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8178, 697, 8111])).
% 1.58/1.51 tff(8180,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s97, c_c2) | (~node3(s97)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s97, c_c2) | (~node3(s97)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8181,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s97, c_c2) | (~node3(s97)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8182,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s97, c_c2) | (~node3(s97))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 1.58/1.51 tff(8183,plain,
% 1.58/1.51 (~node3(s97)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8182, 399, 8179])).
% 1.58/1.51 tff(8184,plain,
% 1.58/1.51 (((~![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(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97)))) <=> ((~![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(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8185,plain,
% 1.58/1.51 (((~node6(s96, s97)) | m_main_v_state1(s96, c_n1) | (~m_main_v_state1(s97, c_n1))) <=> (m_main_v_state1(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8186,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s96, s97)) | m_main_v_state1(s96, c_n1) | (~m_main_v_state1(s97, 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(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97))))),
% 1.58/1.51 inference(monotonicity,[status(thm)],[8185])).
% 1.58/1.51 tff(8187,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s96, s97)) | m_main_v_state1(s96, c_n1) | (~m_main_v_state1(s97, 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(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97)))),
% 1.58/1.51 inference(transitivity,[status(thm)],[8186, 8184])).
% 1.58/1.51 tff(8188,plain,
% 1.58/1.51 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s96, s97)) | m_main_v_state1(s96, c_n1) | (~m_main_v_state1(s97, c_n1)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8189,plain,
% 1.58/1.51 ((~![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(s96, c_n1) | (~m_main_v_state1(s97, c_n1)) | (~node6(s96, s97))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8188, 8187])).
% 1.58/1.51 tff(8190,plain,
% 1.58/1.51 (~m_main_v_state1(s97, c_n1)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8189, 835, 7983, 8068])).
% 1.58/1.51 tff(8191,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s97, c_n1) | (~node2(s97)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s97, c_n1) | (~node2(s97)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8192,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s97, c_n1) | (~node2(s97)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8193,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s97, c_n1) | (~node2(s97))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8192, 8191])).
% 1.58/1.51 tff(8194,plain,
% 1.58/1.51 (~node2(s97)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8193, 787, 8190])).
% 1.58/1.51 tff(8195,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s97, c_t2) | (~node1(s97)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s97, c_t2) | (~node1(s97)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8196,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s97, c_t2) | (~node1(s97)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8197,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s97, c_t2) | (~node1(s97))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8196, 8195])).
% 1.58/1.51 tff(8198,plain,
% 1.58/1.51 (~node1(s97)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8197, 195, 8115])).
% 1.58/1.51 tff(8199,plain,
% 1.58/1.51 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s97, s98)) | node7(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s97, s98)) | node7(s97, s98))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8200,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s97, s98)) | node7(s97, s98))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8201,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s97, s98)) | node7(s97, s98)),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 1.58/1.51 tff(8202,plain,
% 1.58/1.51 (node7(s97, s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8201, 206, 8126])).
% 1.58/1.51 tff(8203,plain,
% 1.58/1.51 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)))) <=> ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8204,plain,
% 1.58/1.51 (((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)) | m_main_v_state1(s98, c_c1)) <=> ((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8205,plain,
% 1.58/1.51 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)) | m_main_v_state1(s98, 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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98))))),
% 1.58/1.51 inference(monotonicity,[status(thm)],[8204])).
% 1.58/1.51 tff(8206,plain,
% 1.58/1.51 (((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)) | m_main_v_state1(s98, 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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)))),
% 1.58/1.51 inference(transitivity,[status(thm)],[8205, 8203])).
% 1.58/1.51 tff(8207,plain,
% 1.58/1.51 ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98)) | m_main_v_state1(s98, c_c1))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8208,plain,
% 1.58/1.51 ((~![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(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97) | (~node7(s97, s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8207, 8206])).
% 1.58/1.51 tff(8209,plain,
% 1.58/1.51 ((~m_main_v_state1(s97, c_t1)) | (~m_main_v_state2(s97, c_n2)) | m_main_v_state1(s98, c_c1) | node1(s97) | node2(s97) | node3(s97)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8208, 892, 8202])).
% 1.58/1.51 tff(8210,plain,
% 1.58/1.51 (m_main_v_state1(s98, c_c1)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8209, 8198, 8111, 8075, 8194, 8183])).
% 1.58/1.51 tff(8211,plain,
% 1.58/1.51 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s98, c_n1)) | (~m_main_v_state1(s98, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s98, c_n1)) | (~m_main_v_state1(s98, c_c1)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8212,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s98, c_n1)) | (~m_main_v_state1(s98, c_c1)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8213,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s98, c_n1)) | (~m_main_v_state1(s98, c_c1))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8212, 8211])).
% 1.58/1.51 tff(8214,plain,
% 1.58/1.51 (~m_main_v_state1(s98, c_n1)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8213, 454, 8210])).
% 1.58/1.51 tff(8215,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s98, c_n1) | (~node11(s98)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s98, c_n1) | (~node11(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8216,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s98, c_n1) | (~node11(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8217,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s98, c_n1) | (~node11(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 1.58/1.51 tff(8218,plain,
% 1.58/1.51 (~node11(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8217, 238, 8214])).
% 1.58/1.51 tff(8219,plain,
% 1.58/1.51 (succ(s98, s99) <=> succ(s98, s99)),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8220,axiom,(succ(s98, s99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound99')).
% 1.58/1.51 tff(8221,plain,
% 1.58/1.51 (succ(s98, s99)),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8220, 8219])).
% 1.58/1.51 tff(8222,plain,
% 1.58/1.51 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8223,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8224,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99)),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 1.58/1.51 tff(8225,plain,
% 1.58/1.51 (trans(s98, s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8224, 8221, 39])).
% 1.58/1.51 tff(8226,plain,
% 1.58/1.51 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s98, s99)) | node14(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s98, s99)) | node14(s98, s99))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8227,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s98, s99)) | node14(s98, s99))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8228,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s98, s99)) | node14(s98, s99)),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8227, 8226])).
% 1.58/1.51 tff(8229,plain,
% 1.58/1.51 (node14(s98, s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8228, 7, 8225])).
% 1.58/1.51 tff(8230,plain,
% 1.58/1.51 (((~![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(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99) | (~node14(s98, s99)))) <=> ((~![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(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99) | (~node14(s98, s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8231,plain,
% 1.58/1.51 ((~![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(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99) | (~node14(s98, s99)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8232,plain,
% 1.58/1.51 ((~![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(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99) | (~node14(s98, s99))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8231, 8230])).
% 1.58/1.51 tff(8233,plain,
% 1.58/1.51 (m_main_v_state2(s98, c_c2) | node9(s98) | node8(s98) | node10(s98) | node11(s98) | node12(s98) | node13(s98, s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8232, 296, 8229])).
% 1.58/1.51 tff(8234,plain,
% 1.58/1.51 (node13(s98, s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8233, 8218, 8175, 8171, 8167, 8163, 8146])).
% 1.58/1.51 tff(8235,plain,
% 1.58/1.51 (((~![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(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99)))) <=> ((~![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(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8236,plain,
% 1.58/1.51 (((~node13(s98, s99)) | m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, c_n2))) <=> (m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8237,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s98, s99)) | m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, 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(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99))))),
% 1.58/1.51 inference(monotonicity,[status(thm)],[8236])).
% 1.58/1.51 tff(8238,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s98, s99)) | m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, 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(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99)))),
% 1.58/1.51 inference(transitivity,[status(thm)],[8237, 8235])).
% 1.58/1.51 tff(8239,plain,
% 1.58/1.51 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s98, s99)) | m_main_v_state2(s98, c_n2) | (~m_main_v_state2(s99, c_n2)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8240,plain,
% 1.58/1.51 ((~![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(s98, c_n2) | (~m_main_v_state2(s99, c_n2)) | (~node13(s98, s99))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8239, 8238])).
% 1.58/1.51 tff(8241,plain,
% 1.58/1.51 (~m_main_v_state2(s99, c_n2)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8240, 311, 8159, 8234])).
% 1.58/1.51 tff(8242,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s99, c_n2) | (~node9(s99)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s99, c_n2) | (~node9(s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8243,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s99, c_n2) | (~node9(s99)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8244,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s99, c_n2) | (~node9(s99))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8243, 8242])).
% 1.58/1.51 tff(8245,plain,
% 1.58/1.51 (~node9(s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8244, 88, 8241])).
% 1.58/1.51 tff(8246,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s99, c_n2) | (~node10(s99)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s99, c_n2) | (~node10(s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8247,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s99, c_n2) | (~node10(s99)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8248,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s99, c_n2) | (~node10(s99))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8247, 8246])).
% 1.58/1.51 tff(8249,plain,
% 1.58/1.51 (~node10(s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8248, 249, 8241])).
% 1.58/1.51 tff(8250,plain,
% 1.58/1.51 (((~![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(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99)))) <=> ((~![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(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8251,plain,
% 1.58/1.51 (((~node13(s98, s99)) | (~m_main_v_state2(s98, c_t2)) | m_main_v_state2(s99, c_t2)) <=> ((~m_main_v_state2(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8252,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s98, s99)) | (~m_main_v_state2(s98, c_t2)) | m_main_v_state2(s99, 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(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99))))),
% 1.58/1.51 inference(monotonicity,[status(thm)],[8251])).
% 1.58/1.51 tff(8253,plain,
% 1.58/1.51 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s98, s99)) | (~m_main_v_state2(s98, c_t2)) | m_main_v_state2(s99, 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(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99)))),
% 1.58/1.51 inference(transitivity,[status(thm)],[8252, 8250])).
% 1.58/1.51 tff(8254,plain,
% 1.58/1.51 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s98, s99)) | (~m_main_v_state2(s98, c_t2)) | m_main_v_state2(s99, c_t2))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8255,plain,
% 1.58/1.51 ((~![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(s98, c_t2)) | m_main_v_state2(s99, c_t2) | (~node13(s98, s99))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8254, 8253])).
% 1.58/1.51 tff(8256,plain,
% 1.58/1.51 (m_main_v_state2(s99, c_t2)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8255, 518, 8155, 8234])).
% 1.58/1.51 tff(8257,plain,
% 1.58/1.51 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s98, c_t1)) | (~m_main_v_state1(s98, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s98, c_t1)) | (~m_main_v_state1(s98, c_c1)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8258,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s98, c_t1)) | (~m_main_v_state1(s98, c_c1)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8259,plain,
% 1.58/1.51 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s98, c_t1)) | (~m_main_v_state1(s98, c_c1))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8258, 8257])).
% 1.58/1.51 tff(8260,plain,
% 1.58/1.51 (~m_main_v_state1(s98, c_t1)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8259, 539, 8210])).
% 1.58/1.51 tff(8261,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s98, c_t1) | (~node5(s98)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s98, c_t1) | (~node5(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8262,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s98, c_t1) | (~node5(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8263,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s98, c_t1) | (~node5(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8262, 8261])).
% 1.58/1.51 tff(8264,plain,
% 1.58/1.51 (~node5(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8263, 550, 8260])).
% 1.58/1.51 tff(8265,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s98, c_n2) | (~node4(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s98, c_n2) | (~node4(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8266,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s98, c_n2) | (~node4(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8267,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s98, c_n2) | (~node4(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8266, 8265])).
% 1.58/1.51 tff(8268,plain,
% 1.58/1.51 (~node4(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8267, 388, 8159])).
% 1.58/1.51 tff(8269,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s98, c_c2) | (~node3(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s98, c_c2) | (~node3(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8270,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s98, c_c2) | (~node3(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8271,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s98, c_c2) | (~node3(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8270, 8269])).
% 1.58/1.51 tff(8272,plain,
% 1.58/1.51 (~node3(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8271, 399, 8175])).
% 1.58/1.51 tff(8273,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s98, c_n2) | (~node2(s98)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s98, c_n2) | (~node2(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8274,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s98, c_n2) | (~node2(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8275,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s98, c_n2) | (~node2(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8274, 8273])).
% 1.58/1.51 tff(8276,plain,
% 1.58/1.51 (~node2(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8275, 410, 8159])).
% 1.58/1.51 tff(8277,plain,
% 1.58/1.51 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s98, c_n1) | (~node1(s98)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s98, c_n1) | (~node1(s98)))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8278,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s98, c_n1) | (~node1(s98)))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8279,plain,
% 1.58/1.51 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s98, c_n1) | (~node1(s98))),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8278, 8277])).
% 1.58/1.51 tff(8280,plain,
% 1.58/1.51 (~node1(s98)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8279, 421, 8214])).
% 1.58/1.51 tff(8281,plain,
% 1.58/1.51 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s98, s99)) | node7(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s98, s99)) | node7(s98, s99))),
% 1.58/1.51 inference(rewrite,[status(thm)],[])).
% 1.58/1.51 tff(8282,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s98, s99)) | node7(s98, s99))),
% 1.58/1.51 inference(quant_inst,[status(thm)],[])).
% 1.58/1.51 tff(8283,plain,
% 1.58/1.51 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s98, s99)) | node7(s98, s99)),
% 1.58/1.51 inference(modus_ponens,[status(thm)],[8282, 8281])).
% 1.58/1.51 tff(8284,plain,
% 1.58/1.51 (node7(s98, s99)),
% 1.58/1.51 inference(unit_resolution,[status(thm)],[8283, 206, 8225])).
% 1.58/1.51 tff(8285,plain,
% 1.58/1.51 (((~![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(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)))) <=> ((~![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(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8286,plain,
% 1.58/1.52 (((~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)) | m_main_v_state1(s99, c_n1)) <=> (m_main_v_state1(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8287,plain,
% 1.58/1.52 (((~![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(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)) | m_main_v_state1(s99, 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(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99))))),
% 1.58/1.52 inference(monotonicity,[status(thm)],[8286])).
% 1.58/1.52 tff(8288,plain,
% 1.58/1.52 (((~![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(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)) | m_main_v_state1(s99, 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(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)))),
% 1.58/1.52 inference(transitivity,[status(thm)],[8287, 8285])).
% 1.58/1.52 tff(8289,plain,
% 1.58/1.52 ((~![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(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99)) | m_main_v_state1(s99, c_n1))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8290,plain,
% 1.58/1.52 ((~![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(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98) | (~node7(s98, s99))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8289, 8288])).
% 1.58/1.52 tff(8291,plain,
% 1.58/1.52 (m_main_v_state1(s99, c_n1) | (~m_main_v_state1(s98, c_c1)) | node1(s98) | node2(s98) | node3(s98) | node4(s98) | node5(s98)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8290, 584, 8284])).
% 1.58/1.52 tff(8292,plain,
% 1.58/1.52 (m_main_v_state1(s99, c_n1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8291, 8280, 8210, 8276, 8272, 8268, 8264])).
% 1.58/1.52 tff(8293,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s99, c_n2) | (~node8(s99)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s99, c_n2) | (~node8(s99)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8294,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s99, c_n2) | (~node8(s99)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8295,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s99, c_n2) | (~node8(s99))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8294, 8293])).
% 1.58/1.52 tff(8296,plain,
% 1.58/1.52 (~node8(s99)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8295, 271, 8241])).
% 1.58/1.52 tff(8297,plain,
% 1.58/1.52 (succ(s99, s100) <=> succ(s99, s100)),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8298,axiom,(succ(s99, s100)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound100')).
% 1.58/1.52 tff(8299,plain,
% 1.58/1.52 (succ(s99, s100)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8298, 8297])).
% 1.58/1.52 tff(8300,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s99, s100)) | trans(s99, s100))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s99, s100)) | trans(s99, s100))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8301,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s99, s100)) | trans(s99, s100))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8302,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s99, s100)) | trans(s99, s100)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8301, 8300])).
% 1.58/1.52 tff(8303,plain,
% 1.58/1.52 (trans(s99, s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8302, 8299, 39])).
% 1.58/1.52 tff(8304,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s99, s100)) | node14(s99, s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s99, s100)) | node14(s99, s100))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8305,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s99, s100)) | node14(s99, s100))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8306,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s99, s100)) | node14(s99, s100)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8305, 8304])).
% 1.58/1.52 tff(8307,plain,
% 1.58/1.52 (node14(s99, s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8306, 7, 8303])).
% 1.58/1.52 tff(8308,plain,
% 1.58/1.52 (((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | (~node14(s99, s100)) | m_main_v_state2(s100, 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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | (~node14(s99, s100)) | m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8309,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | (~node14(s99, s100)) | m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8310,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | (~node14(s99, s100)) | m_main_v_state2(s100, c_c2)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8309, 8308])).
% 1.58/1.52 tff(8311,plain,
% 1.58/1.52 ((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | node9(s99) | node8(s99) | node10(s99) | m_main_v_state2(s100, c_c2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8310, 617, 8307])).
% 1.58/1.52 tff(8312,plain,
% 1.58/1.52 (m_main_v_state2(s100, c_c2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8311, 8296, 8292, 8256, 8249, 8245])).
% 1.58/1.52 tff(8313,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s100, c_t2)) | (~m_main_v_state2(s100, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s100, c_t2)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8314,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s100, c_t2)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8315,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s100, c_t2)) | (~m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8314, 8313])).
% 1.58/1.52 tff(8316,plain,
% 1.58/1.52 (~m_main_v_state2(s100, c_t2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8315, 260, 8312])).
% 1.58/1.52 tff(8317,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s100, c_t2) | (~node12(s100)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s100, c_t2) | (~node12(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8318,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s100, c_t2) | (~node12(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8319,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s100, c_t2) | (~node12(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8318, 8317])).
% 1.58/1.52 tff(8320,plain,
% 1.58/1.52 (~node12(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8319, 633, 8316])).
% 1.58/1.52 tff(8321,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s99, s100)) | node7(s99, s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s99, s100)) | node7(s99, s100))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8322,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s99, s100)) | node7(s99, s100))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8323,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s99, s100)) | node7(s99, s100)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 1.58/1.52 tff(8324,plain,
% 1.58/1.52 (node7(s99, s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8323, 206, 8303])).
% 1.58/1.52 tff(8325,plain,
% 1.58/1.52 (((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node7(s99, s100)) | m_main_v_state1(s100, 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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node7(s99, s100)) | m_main_v_state1(s100, c_t1))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8326,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node7(s99, s100)) | m_main_v_state1(s100, c_t1))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8327,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node7(s99, s100)) | m_main_v_state1(s100, c_t1)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8326, 8325])).
% 1.58/1.52 tff(8328,plain,
% 1.58/1.52 ((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | m_main_v_state1(s100, c_t1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8327, 651, 8324])).
% 1.58/1.52 tff(8329,plain,
% 1.58/1.52 (m_main_v_state1(s100, c_t1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8328, 8256, 8292])).
% 1.58/1.52 tff(8330,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s100, c_n1)) | (~m_main_v_state1(s100, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s100, c_n1)) | (~m_main_v_state1(s100, c_t1)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8331,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s100, c_n1)) | (~m_main_v_state1(s100, c_t1)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8332,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s100, c_n1)) | (~m_main_v_state1(s100, c_t1))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8331, 8330])).
% 1.58/1.52 tff(8333,plain,
% 1.58/1.52 (~m_main_v_state1(s100, c_n1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8332, 17, 8329])).
% 1.58/1.52 tff(8334,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s100, c_n1) | (~node11(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s100, c_n1) | (~node11(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8335,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s100, c_n1) | (~node11(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8336,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s100, c_n1) | (~node11(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8335, 8334])).
% 1.58/1.52 tff(8337,plain,
% 1.58/1.52 (~node11(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8336, 238, 8333])).
% 1.58/1.52 tff(8338,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s100, c_t1)) | (~m_main_v_state1(s100, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s100, c_t1)) | (~m_main_v_state1(s100, c_c1)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8339,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s100, c_t1)) | (~m_main_v_state1(s100, c_c1)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8340,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s100, c_t1)) | (~m_main_v_state1(s100, c_c1))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8339, 8338])).
% 1.58/1.52 tff(8341,plain,
% 1.58/1.52 (~m_main_v_state1(s100, c_c1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8340, 539, 8329])).
% 1.58/1.52 tff(8342,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s100, c_c1) | (~node10(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s100, c_c1) | (~node10(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8343,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s100, c_c1) | (~node10(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8344,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s100, c_c1) | (~node10(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8343, 8342])).
% 1.58/1.52 tff(8345,plain,
% 1.58/1.52 (~node10(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8344, 675, 8341])).
% 1.58/1.52 tff(8346,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s100, c_n1) | (~node9(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s100, c_n1) | (~node9(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8347,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s100, c_n1) | (~node9(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8348,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s100, c_n1) | (~node9(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8347, 8346])).
% 1.58/1.52 tff(8349,plain,
% 1.58/1.52 (~node9(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8348, 686, 8333])).
% 1.58/1.52 tff(8350,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s100, c_n2)) | (~m_main_v_state2(s100, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s100, c_n2)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8351,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s100, c_n2)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8352,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s100, c_n2)) | (~m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8351, 8350])).
% 1.58/1.52 tff(8353,plain,
% 1.58/1.52 (~m_main_v_state2(s100, c_n2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8352, 697, 8312])).
% 1.58/1.52 tff(8354,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s100, c_n2) | (~node8(s100)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s100, c_n2) | (~node8(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8355,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s100, c_n2) | (~node8(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8356,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s100, c_n2) | (~node8(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8355, 8354])).
% 1.58/1.52 tff(8357,plain,
% 1.58/1.52 (~node8(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8356, 271, 8353])).
% 1.58/1.52 tff(8358,plain,
% 1.58/1.52 (succ(s100, s101) <=> succ(s100, s101)),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8359,axiom,(succ(s100, s101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound101')).
% 1.58/1.52 tff(8360,plain,
% 1.58/1.52 (succ(s100, s101)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8359, 8358])).
% 1.58/1.52 tff(8361,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s100, s101)) | trans(s100, s101))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s100, s101)) | trans(s100, s101))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8362,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s100, s101)) | trans(s100, s101))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8363,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s100, s101)) | trans(s100, s101)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8362, 8361])).
% 1.58/1.52 tff(8364,plain,
% 1.58/1.52 (trans(s100, s101)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8363, 8360, 39])).
% 1.58/1.52 tff(8365,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s100, s101)) | node14(s100, s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s100, s101)) | node14(s100, s101))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8366,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s100, s101)) | node14(s100, s101))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8367,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s100, s101)) | node14(s100, s101)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8366, 8365])).
% 1.58/1.52 tff(8368,plain,
% 1.58/1.52 (node14(s100, s101)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8367, 7, 8364])).
% 1.58/1.52 tff(8369,plain,
% 1.58/1.52 (((~![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(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, 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(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8370,plain,
% 1.58/1.52 (((~m_main_v_state2(s100, c_c2)) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | m_main_v_state2(s101, c_n2)) <=> (m_main_v_state2(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8371,plain,
% 1.58/1.52 (((~![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(s100, c_c2)) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | m_main_v_state2(s101, 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(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, c_c2))))),
% 1.58/1.52 inference(monotonicity,[status(thm)],[8370])).
% 1.58/1.52 tff(8372,plain,
% 1.58/1.52 (((~![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(s100, c_c2)) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | m_main_v_state2(s101, 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(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, c_c2)))),
% 1.58/1.52 inference(transitivity,[status(thm)],[8371, 8369])).
% 1.58/1.52 tff(8373,plain,
% 1.58/1.52 ((~![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(s100, c_c2)) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | m_main_v_state2(s101, c_n2))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8374,plain,
% 1.58/1.52 ((~![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(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~node14(s100, s101)) | (~m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8373, 8372])).
% 1.58/1.52 tff(8375,plain,
% 1.58/1.52 (m_main_v_state2(s101, c_n2) | node9(s100) | node8(s100) | node10(s100) | node11(s100) | node12(s100) | (~m_main_v_state2(s100, c_c2))),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8374, 726, 8368])).
% 1.58/1.52 tff(8376,plain,
% 1.58/1.52 (m_main_v_state2(s101, c_n2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8375, 8357, 8312, 8349, 8345, 8337, 8320])).
% 1.58/1.52 tff(8377,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_c2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8378,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_c2)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8379,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_c2))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8378, 8377])).
% 1.58/1.52 tff(8380,plain,
% 1.58/1.52 (~m_main_v_state2(s101, c_c2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8379, 697, 8376])).
% 1.58/1.52 tff(8381,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s101, c_c2) | (~node3(s101)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s101, c_c2) | (~node3(s101)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8382,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s101, c_c2) | (~node3(s101)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8383,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s101, c_c2) | (~node3(s101))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8382, 8381])).
% 1.58/1.52 tff(8384,plain,
% 1.58/1.52 (~node3(s101)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8383, 399, 8380])).
% 1.58/1.52 tff(8385,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s100, c_n1) | (~node1(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s100, c_n1) | (~node1(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8386,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s100, c_n1) | (~node1(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8387,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s100, c_n1) | (~node1(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8386, 8385])).
% 1.58/1.52 tff(8388,plain,
% 1.58/1.52 (~node1(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8387, 421, 8333])).
% 1.58/1.52 tff(8389,plain,
% 1.58/1.52 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s100)) | node18(s99, s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s100)) | node18(s99, s100))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8390,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s99, s100)) | node18(s99, s100))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8391,plain,
% 1.58/1.52 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s99, s100)) | node18(s99, s100)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 1.58/1.52 tff(8392,plain,
% 1.58/1.52 (node18(s99, s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8391, 125, 8303])).
% 1.58/1.52 tff(8393,plain,
% 1.58/1.52 (((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s100)) | m_main_v_turn(s100, 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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s100)) | m_main_v_turn(s100, c_2))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8394,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s100)) | m_main_v_turn(s100, c_2))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8395,plain,
% 1.58/1.52 ((~![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(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | (~node18(s99, s100)) | m_main_v_turn(s100, c_2)),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8394, 8393])).
% 1.58/1.52 tff(8396,plain,
% 1.58/1.52 ((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state2(s99, c_t2)) | m_main_v_turn(s100, c_2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8395, 760, 8392])).
% 1.58/1.52 tff(8397,plain,
% 1.58/1.52 (m_main_v_turn(s100, c_2)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8396, 8256, 8292])).
% 1.58/1.52 tff(8398,plain,
% 1.58/1.52 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s100, c_1)) | (~m_main_v_turn(s100, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s100, c_1)) | (~m_main_v_turn(s100, c_2)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8399,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s100, c_1)) | (~m_main_v_turn(s100, c_2)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8400,plain,
% 1.58/1.52 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s100, c_1)) | (~m_main_v_turn(s100, c_2))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8399, 8398])).
% 1.58/1.52 tff(8401,plain,
% 1.58/1.52 (~m_main_v_turn(s100, c_1)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8400, 156, 8397])).
% 1.58/1.52 tff(8402,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s100, c_1) | (~node5(s100)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s100, c_1) | (~node5(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8403,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | (m_main_v_turn(s100, c_1) | (~node5(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.52 tff(8404,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_turn(X, c_1) | (~node5(X)))) | m_main_v_turn(s100, c_1) | (~node5(s100))),
% 1.58/1.52 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 1.58/1.52 tff(8405,plain,
% 1.58/1.52 (~node5(s100)),
% 1.58/1.52 inference(unit_resolution,[status(thm)],[8404, 776, 8401])).
% 1.58/1.52 tff(8406,plain,
% 1.58/1.52 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s100, c_n1) | (~node2(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s100, c_n1) | (~node2(s100)))),
% 1.58/1.52 inference(rewrite,[status(thm)],[])).
% 1.58/1.52 tff(8407,plain,
% 1.58/1.52 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s100, c_n1) | (~node2(s100)))),
% 1.58/1.52 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8408,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s100, c_n1) | (~node2(s100))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8407, 8406])).
% 1.58/1.53 tff(8409,plain,
% 1.58/1.53 (~node2(s100)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8408, 787, 8333])).
% 1.58/1.53 tff(8410,plain,
% 1.58/1.53 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s100, c_n1) | (~node3(s100)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s100, c_n1) | (~node3(s100)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8411,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | (m_main_v_state1(s100, c_n1) | (~node3(s100)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8412,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node3(X)))) | m_main_v_state1(s100, c_n1) | (~node3(s100))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8411, 8410])).
% 1.58/1.53 tff(8413,plain,
% 1.58/1.53 (~node3(s100)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8412, 798, 8333])).
% 1.58/1.53 tff(8414,plain,
% 1.58/1.53 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s100, c_n2) | (~node4(s100)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s100, c_n2) | (~node4(s100)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8415,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s100, c_n2) | (~node4(s100)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8416,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s100, c_n2) | (~node4(s100))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 1.58/1.53 tff(8417,plain,
% 1.58/1.53 (~node4(s100)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8416, 388, 8353])).
% 1.58/1.53 tff(8418,plain,
% 1.58/1.53 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s100, s101)) | node7(s100, s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s100, s101)) | node7(s100, s101))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8419,plain,
% 1.58/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s100, s101)) | node7(s100, s101))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8420,plain,
% 1.58/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s100, s101)) | node7(s100, s101)),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8419, 8418])).
% 1.58/1.53 tff(8421,plain,
% 1.58/1.53 (node7(s100, s101)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8420, 206, 8364])).
% 1.58/1.53 tff(8422,plain,
% 1.58/1.53 (((~![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(s100, c_c1) | node1(s100) | node2(s100) | node3(s100) | node4(s100) | node5(s100) | node6(s100, s101) | (~node7(s100, s101)))) <=> ((~![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(s100, c_c1) | node1(s100) | node2(s100) | node3(s100) | node4(s100) | node5(s100) | node6(s100, s101) | (~node7(s100, s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8423,plain,
% 1.58/1.53 ((~![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(s100, c_c1) | node1(s100) | node2(s100) | node3(s100) | node4(s100) | node5(s100) | node6(s100, s101) | (~node7(s100, s101)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8424,plain,
% 1.58/1.53 ((~![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(s100, c_c1) | node1(s100) | node2(s100) | node3(s100) | node4(s100) | node5(s100) | node6(s100, s101) | (~node7(s100, s101))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 1.58/1.53 tff(8425,plain,
% 1.58/1.53 (m_main_v_state1(s100, c_c1) | node1(s100) | node2(s100) | node3(s100) | node4(s100) | node5(s100) | node6(s100, s101)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8424, 820, 8421])).
% 1.58/1.53 tff(8426,plain,
% 1.58/1.53 (node6(s100, s101)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8425, 8417, 8341, 8413, 8409, 8405, 8388])).
% 1.58/1.53 tff(8427,plain,
% 1.58/1.53 (((~![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(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101)))) <=> ((~![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(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8428,plain,
% 1.58/1.53 (((~node6(s100, s101)) | m_main_v_state1(s100, c_n1) | (~m_main_v_state1(s101, c_n1))) <=> (m_main_v_state1(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8429,plain,
% 1.58/1.53 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s100, s101)) | m_main_v_state1(s100, c_n1) | (~m_main_v_state1(s101, 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(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101))))),
% 1.58/1.53 inference(monotonicity,[status(thm)],[8428])).
% 1.58/1.53 tff(8430,plain,
% 1.58/1.53 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s100, s101)) | m_main_v_state1(s100, c_n1) | (~m_main_v_state1(s101, 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(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101)))),
% 1.58/1.53 inference(transitivity,[status(thm)],[8429, 8427])).
% 1.58/1.53 tff(8431,plain,
% 1.58/1.53 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | m_main_v_state1(X, V) | (~m_main_v_state1(Y, V)))) | ((~node6(s100, s101)) | m_main_v_state1(s100, c_n1) | (~m_main_v_state1(s101, c_n1)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8432,plain,
% 1.58/1.53 ((~![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(s100, c_n1) | (~m_main_v_state1(s101, c_n1)) | (~node6(s100, s101))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8431, 8430])).
% 1.58/1.53 tff(8433,plain,
% 1.58/1.53 (~m_main_v_state1(s101, c_n1)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8432, 835, 8333, 8426])).
% 1.58/1.53 tff(8434,plain,
% 1.58/1.53 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s101, c_n1) | (~node2(s101)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s101, c_n1) | (~node2(s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8435,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | (m_main_v_state1(s101, c_n1) | (~node2(s101)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8436,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node2(X)))) | m_main_v_state1(s101, c_n1) | (~node2(s101))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8435, 8434])).
% 1.58/1.53 tff(8437,plain,
% 1.58/1.53 (~node2(s101)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8436, 787, 8433])).
% 1.58/1.53 tff(8438,plain,
% 1.58/1.53 (((~![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(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101)))) <=> ((~![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(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8439,plain,
% 1.58/1.53 (((~node6(s100, s101)) | (~m_main_v_state1(s100, c_t1)) | m_main_v_state1(s101, c_t1)) <=> ((~m_main_v_state1(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8440,plain,
% 1.58/1.53 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s100, s101)) | (~m_main_v_state1(s100, c_t1)) | m_main_v_state1(s101, 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(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101))))),
% 1.58/1.53 inference(monotonicity,[status(thm)],[8439])).
% 1.58/1.53 tff(8441,plain,
% 1.58/1.53 (((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s100, s101)) | (~m_main_v_state1(s100, c_t1)) | m_main_v_state1(s101, 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(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101)))),
% 1.58/1.53 inference(transitivity,[status(thm)],[8440, 8438])).
% 1.58/1.53 tff(8442,plain,
% 1.58/1.53 ((~![V: $i, Y: $i, X: $i] : ((~node6(X, Y)) | (~m_main_v_state1(X, V)) | m_main_v_state1(Y, V))) | ((~node6(s100, s101)) | (~m_main_v_state1(s100, c_t1)) | m_main_v_state1(s101, c_t1))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8443,plain,
% 1.58/1.53 ((~![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(s100, c_t1)) | m_main_v_state1(s101, c_t1) | (~node6(s100, s101))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8442, 8441])).
% 1.58/1.53 tff(8444,plain,
% 1.58/1.53 (m_main_v_state1(s101, c_t1)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8443, 856, 8329, 8426])).
% 1.58/1.53 tff(8445,plain,
% 1.58/1.53 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_t2)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8446,plain,
% 1.58/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_t2)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8447,plain,
% 1.58/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s101, c_n2)) | (~m_main_v_state2(s101, c_t2))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8446, 8445])).
% 1.58/1.53 tff(8448,plain,
% 1.58/1.53 (~m_main_v_state2(s101, c_t2)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8447, 77, 8376])).
% 1.58/1.53 tff(8449,plain,
% 1.58/1.53 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s101, c_t2) | (~node1(s101)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s101, c_t2) | (~node1(s101)))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8450,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | (m_main_v_state2(s101, c_t2) | (~node1(s101)))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8451,plain,
% 1.58/1.53 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node1(X)))) | m_main_v_state2(s101, c_t2) | (~node1(s101))),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8450, 8449])).
% 1.58/1.53 tff(8452,plain,
% 1.58/1.53 (~node1(s101)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8451, 195, 8448])).
% 1.58/1.53 tff(8453,plain,
% 1.58/1.53 (succ(s101, s102) <=> succ(s101, s102)),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8454,axiom,(succ(s101, s102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound102')).
% 1.58/1.53 tff(8455,plain,
% 1.58/1.53 (succ(s101, s102)),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8454, 8453])).
% 1.58/1.53 tff(8456,plain,
% 1.58/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s101, s102)) | trans(s101, s102))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s101, s102)) | trans(s101, s102))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8457,plain,
% 1.58/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s101, s102)) | trans(s101, s102))),
% 1.58/1.53 inference(quant_inst,[status(thm)],[])).
% 1.58/1.53 tff(8458,plain,
% 1.58/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s101, s102)) | trans(s101, s102)),
% 1.58/1.53 inference(modus_ponens,[status(thm)],[8457, 8456])).
% 1.58/1.53 tff(8459,plain,
% 1.58/1.53 (trans(s101, s102)),
% 1.58/1.53 inference(unit_resolution,[status(thm)],[8458, 8455, 39])).
% 1.58/1.53 tff(8460,plain,
% 1.58/1.53 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s101, s102)) | node7(s101, s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s101, s102)) | node7(s101, s102))),
% 1.58/1.53 inference(rewrite,[status(thm)],[])).
% 1.58/1.53 tff(8461,plain,
% 1.58/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s101, s102)) | node7(s101, s102))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8462,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s101, s102)) | node7(s101, s102)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8461, 8460])).
% 1.61/1.53 tff(8463,plain,
% 1.61/1.53 (node7(s101, s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8462, 206, 8459])).
% 1.61/1.53 tff(8464,plain,
% 1.61/1.53 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)))) <=> ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8465,plain,
% 1.61/1.53 (((~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)) | m_main_v_state1(s102, c_c1)) <=> ((~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8466,plain,
% 1.61/1.53 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)) | m_main_v_state1(s102, 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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102))))),
% 1.61/1.53 inference(monotonicity,[status(thm)],[8465])).
% 1.61/1.53 tff(8467,plain,
% 1.61/1.53 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)) | m_main_v_state1(s102, 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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)))),
% 1.61/1.53 inference(transitivity,[status(thm)],[8466, 8464])).
% 1.61/1.53 tff(8468,plain,
% 1.61/1.53 ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102)) | m_main_v_state1(s102, c_c1))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8469,plain,
% 1.61/1.53 ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101) | (~node7(s101, s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8468, 8467])).
% 1.61/1.53 tff(8470,plain,
% 1.61/1.53 ((~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state1(s102, c_c1) | node1(s101) | node2(s101) | node3(s101)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8469, 892, 8463])).
% 1.61/1.53 tff(8471,plain,
% 1.61/1.53 (m_main_v_state1(s102, c_c1)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8470, 8452, 8376, 8444, 8437, 8384])).
% 1.61/1.53 tff(8472,plain,
% 1.61/1.53 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s102, c_t1)) | (~m_main_v_state1(s102, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s102, c_t1)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8473,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s102, c_t1)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8474,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s102, c_t1)) | (~m_main_v_state1(s102, c_c1))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8473, 8472])).
% 1.61/1.53 tff(8475,plain,
% 1.61/1.53 (~m_main_v_state1(s102, c_t1)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8474, 539, 8471])).
% 1.61/1.53 tff(8476,plain,
% 1.61/1.53 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s102, c_t1) | (~node5(s102)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s102, c_t1) | (~node5(s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8477,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | (m_main_v_state1(s102, c_t1) | (~node5(s102)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8478,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node5(X)))) | m_main_v_state1(s102, c_t1) | (~node5(s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8477, 8476])).
% 1.61/1.53 tff(8479,plain,
% 1.61/1.53 (~node5(s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8478, 550, 8475])).
% 1.61/1.53 tff(8480,plain,
% 1.61/1.53 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s101, s102)) | node14(s101, s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s101, s102)) | node14(s101, s102))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8481,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s101, s102)) | node14(s101, s102))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8482,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s101, s102)) | node14(s101, s102)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8481, 8480])).
% 1.61/1.53 tff(8483,plain,
% 1.61/1.53 (node14(s101, s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8482, 7, 8459])).
% 1.61/1.53 tff(8484,plain,
% 1.61/1.53 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | (~node14(s101, s102)) | m_main_v_state2(s102, 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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | (~node14(s101, s102)) | m_main_v_state2(s102, c_t2))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8485,plain,
% 1.61/1.53 ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | (~node14(s101, s102)) | m_main_v_state2(s102, c_t2))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8486,plain,
% 1.61/1.53 ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | (~node14(s101, s102)) | m_main_v_state2(s102, c_t2)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8485, 8484])).
% 1.61/1.53 tff(8487,plain,
% 1.61/1.53 ((~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_state2(s102, c_t2)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8486, 922, 8483])).
% 1.61/1.53 tff(8488,plain,
% 1.61/1.53 (m_main_v_state2(s102, c_t2)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8487, 8444, 8376])).
% 1.61/1.53 tff(8489,plain,
% 1.61/1.53 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s102, c_n2)) | (~m_main_v_state2(s102, c_t2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s102, c_n2)) | (~m_main_v_state2(s102, c_t2)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8490,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | ((~m_main_v_state2(s102, c_n2)) | (~m_main_v_state2(s102, c_t2)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8491,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_t2)))) | (~m_main_v_state2(s102, c_n2)) | (~m_main_v_state2(s102, c_t2))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8490, 8489])).
% 1.61/1.53 tff(8492,plain,
% 1.61/1.53 (~m_main_v_state2(s102, c_n2)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8491, 77, 8488])).
% 1.61/1.53 tff(8493,plain,
% 1.61/1.53 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s102, c_n2) | (~node4(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s102, c_n2) | (~node4(s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8494,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | (m_main_v_state2(s102, c_n2) | (~node4(s102)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8495,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node4(X)))) | m_main_v_state2(s102, c_n2) | (~node4(s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8494, 8493])).
% 1.61/1.53 tff(8496,plain,
% 1.61/1.53 (~node4(s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8495, 388, 8492])).
% 1.61/1.53 tff(8497,plain,
% 1.61/1.53 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s102, c_t2)) | (~m_main_v_state2(s102, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s102, c_t2)) | (~m_main_v_state2(s102, c_c2)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8498,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s102, c_t2)) | (~m_main_v_state2(s102, c_c2)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8499,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s102, c_t2)) | (~m_main_v_state2(s102, c_c2))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8498, 8497])).
% 1.61/1.53 tff(8500,plain,
% 1.61/1.53 (~m_main_v_state2(s102, c_c2)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8499, 260, 8488])).
% 1.61/1.53 tff(8501,plain,
% 1.61/1.53 (((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s102, c_c2) | (~node3(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s102, c_c2) | (~node3(s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8502,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | (m_main_v_state2(s102, c_c2) | (~node3(s102)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8503,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_c2) | (~node3(X)))) | m_main_v_state2(s102, c_c2) | (~node3(s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 1.61/1.53 tff(8504,plain,
% 1.61/1.53 (~node3(s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8503, 399, 8500])).
% 1.61/1.53 tff(8505,plain,
% 1.61/1.53 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s102, c_n2) | (~node2(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s102, c_n2) | (~node2(s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8506,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | (m_main_v_state2(s102, c_n2) | (~node2(s102)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8507,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node2(X)))) | m_main_v_state2(s102, c_n2) | (~node2(s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8506, 8505])).
% 1.61/1.53 tff(8508,plain,
% 1.61/1.53 (~node2(s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8507, 410, 8492])).
% 1.61/1.53 tff(8509,plain,
% 1.61/1.53 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s102, c_n1)) | (~m_main_v_state1(s102, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s102, c_n1)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8510,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s102, c_n1)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8511,plain,
% 1.61/1.53 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s102, c_n1)) | (~m_main_v_state1(s102, c_c1))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 1.61/1.53 tff(8512,plain,
% 1.61/1.53 (~m_main_v_state1(s102, c_n1)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8511, 454, 8471])).
% 1.61/1.53 tff(8513,plain,
% 1.61/1.53 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s102, c_n1) | (~node1(s102)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s102, c_n1) | (~node1(s102)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8514,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | (m_main_v_state1(s102, c_n1) | (~node1(s102)))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8515,plain,
% 1.61/1.53 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node1(X)))) | m_main_v_state1(s102, c_n1) | (~node1(s102))),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8514, 8513])).
% 1.61/1.53 tff(8516,plain,
% 1.61/1.53 (~node1(s102)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8515, 421, 8512])).
% 1.61/1.53 tff(8517,plain,
% 1.61/1.53 (succ(s102, s103) <=> succ(s102, s103)),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8518,axiom,(succ(s102, s103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound103')).
% 1.61/1.53 tff(8519,plain,
% 1.61/1.53 (succ(s102, s103)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 1.61/1.53 tff(8520,plain,
% 1.61/1.53 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s102, s103)) | trans(s102, s103))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s102, s103)) | trans(s102, s103))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8521,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s102, s103)) | trans(s102, s103))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8522,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s102, s103)) | trans(s102, s103)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8521, 8520])).
% 1.61/1.53 tff(8523,plain,
% 1.61/1.53 (trans(s102, s103)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8522, 8519, 39])).
% 1.61/1.53 tff(8524,plain,
% 1.61/1.53 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s102, s103)) | node7(s102, s103))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s102, s103)) | node7(s102, s103))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8525,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s102, s103)) | node7(s102, s103))),
% 1.61/1.53 inference(quant_inst,[status(thm)],[])).
% 1.61/1.53 tff(8526,plain,
% 1.61/1.53 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s102, s103)) | node7(s102, s103)),
% 1.61/1.53 inference(modus_ponens,[status(thm)],[8525, 8524])).
% 1.61/1.53 tff(8527,plain,
% 1.61/1.53 (node7(s102, s103)),
% 1.61/1.53 inference(unit_resolution,[status(thm)],[8526, 206, 8523])).
% 1.61/1.53 tff(8528,plain,
% 1.61/1.53 (((~![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(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)))) <=> ((~![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(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.53 tff(8529,plain,
% 1.61/1.53 (((~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)) | m_main_v_state1(s103, c_n1)) <=> (m_main_v_state1(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)))),
% 1.61/1.53 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8530,plain,
% 1.61/1.54 (((~![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(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)) | m_main_v_state1(s103, 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(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103))))),
% 1.61/1.54 inference(monotonicity,[status(thm)],[8529])).
% 1.61/1.54 tff(8531,plain,
% 1.61/1.54 (((~![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(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)) | m_main_v_state1(s103, 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(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)))),
% 1.61/1.54 inference(transitivity,[status(thm)],[8530, 8528])).
% 1.61/1.54 tff(8532,plain,
% 1.61/1.54 ((~![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(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103)) | m_main_v_state1(s103, c_n1))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8533,plain,
% 1.61/1.54 ((~![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(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102) | (~node7(s102, s103))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8532, 8531])).
% 1.61/1.54 tff(8534,plain,
% 1.61/1.54 (m_main_v_state1(s103, c_n1) | (~m_main_v_state1(s102, c_c1)) | node1(s102) | node2(s102) | node3(s102) | node4(s102) | node5(s102)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8533, 584, 8527])).
% 1.61/1.54 tff(8535,plain,
% 1.61/1.54 (m_main_v_state1(s103, c_n1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8534, 8516, 8471, 8508, 8504, 8496, 8479])).
% 1.61/1.54 tff(8536,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s103, c_n1)) | (~m_main_v_state1(s103, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s103, c_n1)) | (~m_main_v_state1(s103, c_t1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8537,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s103, c_n1)) | (~m_main_v_state1(s103, c_t1)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8538,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s103, c_n1)) | (~m_main_v_state1(s103, c_t1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8537, 8536])).
% 1.61/1.54 tff(8539,plain,
% 1.61/1.54 (~m_main_v_state1(s103, c_t1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8538, 17, 8535])).
% 1.61/1.54 tff(8540,plain,
% 1.61/1.54 (^[X: $i] : refl((m_main_v_state1(X, c_t1) | (~node20(X))) <=> (m_main_v_state1(X, c_t1) | (~node20(X))))),
% 1.61/1.54 inference(bind,[status(th)],[])).
% 1.61/1.54 tff(8541,plain,
% 1.61/1.54 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))),
% 1.61/1.54 inference(quant_intro,[status(thm)],[8540])).
% 1.61/1.54 tff(8542,plain,
% 1.61/1.54 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X))) <=> ![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8543,axiom,(![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 1.61/1.54 tff(8544,plain,
% 1.61/1.54 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8543, 8542])).
% 1.61/1.54 tff(8545,plain,(
% 1.61/1.54 ![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))),
% 1.61/1.54 inference(skolemize,[status(sab)],[8544])).
% 1.61/1.54 tff(8546,plain,
% 1.61/1.54 (![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8545, 8541])).
% 1.61/1.54 tff(8547,plain,
% 1.61/1.54 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s103, c_t1) | (~node20(s103)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s103, c_t1) | (~node20(s103)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8548,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s103, c_t1) | (~node20(s103)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8549,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s103, c_t1) | (~node20(s103))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 1.61/1.54 tff(8550,plain,
% 1.61/1.54 (~node20(s103)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8549, 8546, 8539])).
% 1.61/1.54 tff(8551,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s102)) | (~m_main_v_state1(s102, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s102)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8552,plain,
% 1.61/1.54 (((~m_main_v_state1(s102, c_c1)) | (~always19(s102))) <=> ((~always19(s102)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8553,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s102, c_c1)) | (~always19(s102)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s102)) | (~m_main_v_state1(s102, c_c1))))),
% 1.61/1.54 inference(monotonicity,[status(thm)],[8552])).
% 1.61/1.54 tff(8554,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s102, c_c1)) | (~always19(s102)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s102)) | (~m_main_v_state1(s102, c_c1)))),
% 1.61/1.54 inference(transitivity,[status(thm)],[8553, 8551])).
% 1.61/1.54 tff(8555,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s102, c_c1)) | (~always19(s102)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8556,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s102)) | (~m_main_v_state1(s102, c_c1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8555, 8554])).
% 1.61/1.54 tff(8557,plain,
% 1.61/1.54 (~always19(s102)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8556, 3439, 8471])).
% 1.61/1.54 tff(8558,plain,
% 1.61/1.54 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~always19(X)) | always19(Y)) <=> ((~trans(X, Y)) | (~always19(X)) | always19(Y)))),
% 1.61/1.54 inference(bind,[status(th)],[])).
% 1.61/1.54 tff(8559,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(quant_intro,[status(thm)],[8558])).
% 1.61/1.54 tff(8560,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8561,plain,
% 1.61/1.54 (^[Y: $i, X: $i] : rewrite(((always19(Y) | (~trans(X, Y))) | (~always19(X))) <=> ((~trans(X, Y)) | (~always19(X)) | always19(Y)))),
% 1.61/1.54 inference(bind,[status(th)],[])).
% 1.61/1.54 tff(8562,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((always19(Y) | (~trans(X, Y))) | (~always19(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(quant_intro,[status(thm)],[8561])).
% 1.61/1.54 tff(8563,axiom,(![Y: $i, X: $i] : ((always19(Y) | (~trans(X, Y))) | (~always19(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 1.61/1.54 tff(8564,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8563, 8562])).
% 1.61/1.54 tff(8565,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8564, 8560])).
% 1.61/1.54 tff(8566,plain,(
% 1.61/1.54 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(skolemize,[status(sab)],[8565])).
% 1.61/1.54 tff(8567,plain,
% 1.61/1.54 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8566, 8559])).
% 1.61/1.54 tff(8568,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s101, s102)) | (~always19(s101)) | always19(s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s101, s102)) | (~always19(s101)) | always19(s102))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8569,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s101, s102)) | (~always19(s101)) | always19(s102))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8570,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s101, s102)) | (~always19(s101)) | always19(s102)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8569, 8568])).
% 1.61/1.54 tff(8571,plain,
% 1.61/1.54 ((~always19(s101)) | always19(s102)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8570, 8567, 8459])).
% 1.61/1.54 tff(8572,plain,
% 1.61/1.54 (~always19(s101)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8571, 8557])).
% 1.61/1.54 tff(8573,plain,
% 1.61/1.54 (^[X: $i] : refl((always19(X) | (~node20(X))) <=> (always19(X) | (~node20(X))))),
% 1.61/1.54 inference(bind,[status(th)],[])).
% 1.61/1.54 tff(8574,plain,
% 1.61/1.54 (![X: $i] : (always19(X) | (~node20(X))) <=> ![X: $i] : (always19(X) | (~node20(X)))),
% 1.61/1.54 inference(quant_intro,[status(thm)],[8573])).
% 1.61/1.54 tff(8575,plain,
% 1.61/1.54 (![X: $i] : (always19(X) | (~node20(X))) <=> ![X: $i] : (always19(X) | (~node20(X)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8576,axiom,(![X: $i] : (always19(X) | (~node20(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 1.61/1.54 tff(8577,plain,
% 1.61/1.54 (![X: $i] : (always19(X) | (~node20(X)))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8576, 8575])).
% 1.61/1.54 tff(8578,plain,(
% 1.61/1.54 ![X: $i] : (always19(X) | (~node20(X)))),
% 1.61/1.54 inference(skolemize,[status(sab)],[8577])).
% 1.61/1.54 tff(8579,plain,
% 1.61/1.54 (![X: $i] : (always19(X) | (~node20(X)))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8578, 8574])).
% 1.61/1.54 tff(8580,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s101) | (~node20(s101)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s101) | (~node20(s101)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8581,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s101) | (~node20(s101)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8582,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s101) | (~node20(s101))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8581, 8580])).
% 1.61/1.54 tff(8583,plain,
% 1.61/1.54 (~node20(s101)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8582, 8579, 8572])).
% 1.61/1.54 tff(8584,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s100, s101)) | (~always19(s100)) | always19(s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s100, s101)) | (~always19(s100)) | always19(s101))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8585,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s100, s101)) | (~always19(s100)) | always19(s101))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8586,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s100, s101)) | (~always19(s100)) | always19(s101)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 1.61/1.54 tff(8587,plain,
% 1.61/1.54 ((~always19(s100)) | always19(s101)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8586, 8567, 8364])).
% 1.61/1.54 tff(8588,plain,
% 1.61/1.54 (~always19(s100)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8587, 8572])).
% 1.61/1.54 tff(8589,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s100) | (~node20(s100)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s100) | (~node20(s100)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8590,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s100) | (~node20(s100)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8591,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s100) | (~node20(s100))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8590, 8589])).
% 1.61/1.54 tff(8592,plain,
% 1.61/1.54 (~node20(s100)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8591, 8579, 8588])).
% 1.61/1.54 tff(8593,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state1(s99, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s99, c_n1)) | (~m_main_v_state1(s99, c_t1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8594,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s99, c_n1)) | (~m_main_v_state1(s99, c_t1)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8595,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s99, c_n1)) | (~m_main_v_state1(s99, c_t1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8594, 8593])).
% 1.61/1.54 tff(8596,plain,
% 1.61/1.54 (~m_main_v_state1(s99, c_t1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8595, 17, 8292])).
% 1.61/1.54 tff(8597,plain,
% 1.61/1.54 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s99, c_t1) | (~node20(s99)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s99, c_t1) | (~node20(s99)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8598,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s99, c_t1) | (~node20(s99)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8599,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s99, c_t1) | (~node20(s99))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8598, 8597])).
% 1.61/1.54 tff(8600,plain,
% 1.61/1.54 (~node20(s99)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8599, 8546, 8596])).
% 1.61/1.54 tff(8601,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s98)) | (~m_main_v_state1(s98, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s98)) | (~m_main_v_state1(s98, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8602,plain,
% 1.61/1.54 (((~m_main_v_state1(s98, c_c1)) | (~always19(s98))) <=> ((~always19(s98)) | (~m_main_v_state1(s98, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8603,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s98, c_c1)) | (~always19(s98)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s98)) | (~m_main_v_state1(s98, c_c1))))),
% 1.61/1.54 inference(monotonicity,[status(thm)],[8602])).
% 1.61/1.54 tff(8604,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s98, c_c1)) | (~always19(s98)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s98)) | (~m_main_v_state1(s98, c_c1)))),
% 1.61/1.54 inference(transitivity,[status(thm)],[8603, 8601])).
% 1.61/1.54 tff(8605,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s98, c_c1)) | (~always19(s98)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8606,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s98)) | (~m_main_v_state1(s98, c_c1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8605, 8604])).
% 1.61/1.54 tff(8607,plain,
% 1.61/1.54 (~always19(s98)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8606, 3439, 8210])).
% 1.61/1.54 tff(8608,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s97, s98)) | (~always19(s97)) | always19(s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s97, s98)) | (~always19(s97)) | always19(s98))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8609,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s97, s98)) | (~always19(s97)) | always19(s98))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8610,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s97, s98)) | (~always19(s97)) | always19(s98)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8609, 8608])).
% 1.61/1.54 tff(8611,plain,
% 1.61/1.54 ((~always19(s97)) | always19(s98)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8610, 8567, 8126])).
% 1.61/1.54 tff(8612,plain,
% 1.61/1.54 (~always19(s97)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8611, 8607])).
% 1.61/1.54 tff(8613,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s97) | (~node20(s97)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s97) | (~node20(s97)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8614,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s97) | (~node20(s97)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8615,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s97) | (~node20(s97))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8614, 8613])).
% 1.61/1.54 tff(8616,plain,
% 1.61/1.54 (~node20(s97)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8615, 8579, 8612])).
% 1.61/1.54 tff(8617,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s96, s97)) | (~always19(s96)) | always19(s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s96, s97)) | (~always19(s96)) | always19(s97))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8618,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s96, s97)) | (~always19(s96)) | always19(s97))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8619,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s96, s97)) | (~always19(s96)) | always19(s97)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8618, 8617])).
% 1.61/1.54 tff(8620,plain,
% 1.61/1.54 ((~always19(s96)) | always19(s97)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8619, 8567, 8059])).
% 1.61/1.54 tff(8621,plain,
% 1.61/1.54 (~always19(s96)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8620, 8612])).
% 1.61/1.54 tff(8622,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s96) | (~node20(s96)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s96) | (~node20(s96)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8623,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s96) | (~node20(s96)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8624,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s96) | (~node20(s96))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8623, 8622])).
% 1.61/1.54 tff(8625,plain,
% 1.61/1.54 (~node20(s96)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8624, 8579, 8621])).
% 1.61/1.54 tff(8626,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state1(s95, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s95, c_n1)) | (~m_main_v_state1(s95, c_t1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8627,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s95, c_n1)) | (~m_main_v_state1(s95, c_t1)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8628,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s95, c_n1)) | (~m_main_v_state1(s95, c_t1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8627, 8626])).
% 1.61/1.54 tff(8629,plain,
% 1.61/1.54 (~m_main_v_state1(s95, c_t1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8628, 17, 7907])).
% 1.61/1.54 tff(8630,plain,
% 1.61/1.54 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s95, c_t1) | (~node20(s95)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s95, c_t1) | (~node20(s95)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8631,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s95, c_t1) | (~node20(s95)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8632,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s95, c_t1) | (~node20(s95))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8631, 8630])).
% 1.61/1.54 tff(8633,plain,
% 1.61/1.54 (~node20(s95)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8632, 8546, 8629])).
% 1.61/1.54 tff(8634,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s94)) | (~m_main_v_state1(s94, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s94)) | (~m_main_v_state1(s94, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8635,plain,
% 1.61/1.54 (((~m_main_v_state1(s94, c_c1)) | (~always19(s94))) <=> ((~always19(s94)) | (~m_main_v_state1(s94, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8636,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s94, c_c1)) | (~always19(s94)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s94)) | (~m_main_v_state1(s94, c_c1))))),
% 1.61/1.54 inference(monotonicity,[status(thm)],[8635])).
% 1.61/1.54 tff(8637,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s94, c_c1)) | (~always19(s94)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s94)) | (~m_main_v_state1(s94, c_c1)))),
% 1.61/1.54 inference(transitivity,[status(thm)],[8636, 8634])).
% 1.61/1.54 tff(8638,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s94, c_c1)) | (~always19(s94)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8639,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s94)) | (~m_main_v_state1(s94, c_c1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8638, 8637])).
% 1.61/1.54 tff(8640,plain,
% 1.61/1.54 (~always19(s94)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8639, 3439, 7843])).
% 1.61/1.54 tff(8641,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s93, s94)) | (~always19(s93)) | always19(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s93, s94)) | (~always19(s93)) | always19(s94))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8642,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s93, s94)) | (~always19(s93)) | always19(s94))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8643,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s93, s94)) | (~always19(s93)) | always19(s94)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8642, 8641])).
% 1.61/1.54 tff(8644,plain,
% 1.61/1.54 ((~always19(s93)) | always19(s94)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8643, 8567, 7831])).
% 1.61/1.54 tff(8645,plain,
% 1.61/1.54 (~always19(s93)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8644, 8640])).
% 1.61/1.54 tff(8646,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s93) | (~node20(s93)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s93) | (~node20(s93)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8647,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s93) | (~node20(s93)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8648,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s93) | (~node20(s93))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8647, 8646])).
% 1.61/1.54 tff(8649,plain,
% 1.61/1.54 (~node20(s93)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8648, 8579, 8645])).
% 1.61/1.54 tff(8650,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s92, s93)) | (~always19(s92)) | always19(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s92, s93)) | (~always19(s92)) | always19(s93))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8651,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s92, s93)) | (~always19(s92)) | always19(s93))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8652,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s92, s93)) | (~always19(s92)) | always19(s93)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8651, 8650])).
% 1.61/1.54 tff(8653,plain,
% 1.61/1.54 ((~always19(s92)) | always19(s93)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8652, 8567, 7736])).
% 1.61/1.54 tff(8654,plain,
% 1.61/1.54 (~always19(s92)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8653, 8645])).
% 1.61/1.54 tff(8655,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s92) | (~node20(s92)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s92) | (~node20(s92)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8656,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s92) | (~node20(s92)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8657,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s92) | (~node20(s92))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8656, 8655])).
% 1.61/1.54 tff(8658,plain,
% 1.61/1.54 (~node20(s92)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8657, 8579, 8654])).
% 1.61/1.54 tff(8659,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state1(s91, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s91, c_n1)) | (~m_main_v_state1(s91, c_t1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8660,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s91, c_n1)) | (~m_main_v_state1(s91, c_t1)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8661,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s91, c_n1)) | (~m_main_v_state1(s91, c_t1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8660, 8659])).
% 1.61/1.54 tff(8662,plain,
% 1.61/1.54 (~m_main_v_state1(s91, c_t1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8661, 17, 7664])).
% 1.61/1.54 tff(8663,plain,
% 1.61/1.54 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s91, c_t1) | (~node20(s91)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s91, c_t1) | (~node20(s91)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8664,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s91, c_t1) | (~node20(s91)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8665,plain,
% 1.61/1.54 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s91, c_t1) | (~node20(s91))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8664, 8663])).
% 1.61/1.54 tff(8666,plain,
% 1.61/1.54 (~node20(s91)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8665, 8546, 8662])).
% 1.61/1.54 tff(8667,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s90)) | (~m_main_v_state1(s90, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s90)) | (~m_main_v_state1(s90, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8668,plain,
% 1.61/1.54 (((~m_main_v_state1(s90, c_c1)) | (~always19(s90))) <=> ((~always19(s90)) | (~m_main_v_state1(s90, c_c1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8669,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s90, c_c1)) | (~always19(s90)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s90)) | (~m_main_v_state1(s90, c_c1))))),
% 1.61/1.54 inference(monotonicity,[status(thm)],[8668])).
% 1.61/1.54 tff(8670,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s90, c_c1)) | (~always19(s90)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s90)) | (~m_main_v_state1(s90, c_c1)))),
% 1.61/1.54 inference(transitivity,[status(thm)],[8669, 8667])).
% 1.61/1.54 tff(8671,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s90, c_c1)) | (~always19(s90)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8672,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s90)) | (~m_main_v_state1(s90, c_c1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8671, 8670])).
% 1.61/1.54 tff(8673,plain,
% 1.61/1.54 (~always19(s90)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8672, 3439, 7582])).
% 1.61/1.54 tff(8674,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s89, s90)) | (~always19(s89)) | always19(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s89, s90)) | (~always19(s89)) | always19(s90))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8675,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s89, s90)) | (~always19(s89)) | always19(s90))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8676,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s89, s90)) | (~always19(s89)) | always19(s90)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8675, 8674])).
% 1.61/1.54 tff(8677,plain,
% 1.61/1.54 ((~always19(s89)) | always19(s90)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8676, 8567, 7498])).
% 1.61/1.54 tff(8678,plain,
% 1.61/1.54 (~always19(s89)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8677, 8673])).
% 1.61/1.54 tff(8679,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s89) | (~node20(s89)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s89) | (~node20(s89)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8680,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s89) | (~node20(s89)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8681,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s89) | (~node20(s89))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8680, 8679])).
% 1.61/1.54 tff(8682,plain,
% 1.61/1.54 (~node20(s89)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8681, 8579, 8678])).
% 1.61/1.54 tff(8683,plain,
% 1.61/1.54 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s88, s89)) | (~always19(s88)) | always19(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s88, s89)) | (~always19(s88)) | always19(s89))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8684,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s88, s89)) | (~always19(s88)) | always19(s89))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8685,plain,
% 1.61/1.54 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s88, s89)) | (~always19(s88)) | always19(s89)),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8684, 8683])).
% 1.61/1.54 tff(8686,plain,
% 1.61/1.54 ((~always19(s88)) | always19(s89)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8685, 8567, 7431])).
% 1.61/1.54 tff(8687,plain,
% 1.61/1.54 (~always19(s88)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8686, 8678])).
% 1.61/1.54 tff(8688,plain,
% 1.61/1.54 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s88) | (~node20(s88)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s88) | (~node20(s88)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8689,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s88) | (~node20(s88)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8690,plain,
% 1.61/1.54 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s88) | (~node20(s88))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8689, 8688])).
% 1.61/1.54 tff(8691,plain,
% 1.61/1.54 (~node20(s88)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8690, 8579, 8687])).
% 1.61/1.54 tff(8692,plain,
% 1.61/1.54 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state1(s87, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s87, c_n1)) | (~m_main_v_state1(s87, c_t1)))),
% 1.61/1.54 inference(rewrite,[status(thm)],[])).
% 1.61/1.54 tff(8693,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s87, c_n1)) | (~m_main_v_state1(s87, c_t1)))),
% 1.61/1.54 inference(quant_inst,[status(thm)],[])).
% 1.61/1.54 tff(8694,plain,
% 1.61/1.54 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s87, c_n1)) | (~m_main_v_state1(s87, c_t1))),
% 1.61/1.54 inference(modus_ponens,[status(thm)],[8693, 8692])).
% 1.61/1.54 tff(8695,plain,
% 1.61/1.54 (~m_main_v_state1(s87, c_t1)),
% 1.61/1.54 inference(unit_resolution,[status(thm)],[8694, 17, 7279])).
% 1.61/1.54 tff(8696,plain,
% 1.61/1.54 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s87, c_t1) | (~node20(s87)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s87, c_t1) | (~node20(s87)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8697,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s87, c_t1) | (~node20(s87)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8698,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s87, c_t1) | (~node20(s87))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8697, 8696])).
% 1.61/1.55 tff(8699,plain,
% 1.61/1.55 (~node20(s87)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8698, 8546, 8695])).
% 1.61/1.55 tff(8700,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s86)) | (~m_main_v_state1(s86, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s86)) | (~m_main_v_state1(s86, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8701,plain,
% 1.61/1.55 (((~m_main_v_state1(s86, c_c1)) | (~always19(s86))) <=> ((~always19(s86)) | (~m_main_v_state1(s86, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8702,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s86, c_c1)) | (~always19(s86)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s86)) | (~m_main_v_state1(s86, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8701])).
% 1.61/1.55 tff(8703,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s86, c_c1)) | (~always19(s86)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s86)) | (~m_main_v_state1(s86, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8702, 8700])).
% 1.61/1.55 tff(8704,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s86, c_c1)) | (~always19(s86)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8705,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s86)) | (~m_main_v_state1(s86, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8704, 8703])).
% 1.61/1.55 tff(8706,plain,
% 1.61/1.55 (~always19(s86)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8705, 3439, 7215])).
% 1.61/1.55 tff(8707,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s85, s86)) | (~always19(s85)) | always19(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s85, s86)) | (~always19(s85)) | always19(s86))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8708,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s85, s86)) | (~always19(s85)) | always19(s86))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8709,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s85, s86)) | (~always19(s85)) | always19(s86)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8708, 8707])).
% 1.61/1.55 tff(8710,plain,
% 1.61/1.55 ((~always19(s85)) | always19(s86)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8709, 8567, 7203])).
% 1.61/1.55 tff(8711,plain,
% 1.61/1.55 (~always19(s85)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8710, 8706])).
% 1.61/1.55 tff(8712,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s85) | (~node20(s85)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s85) | (~node20(s85)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8713,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s85) | (~node20(s85)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8714,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s85) | (~node20(s85))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8713, 8712])).
% 1.61/1.55 tff(8715,plain,
% 1.61/1.55 (~node20(s85)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8714, 8579, 8711])).
% 1.61/1.55 tff(8716,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s84, s85)) | (~always19(s84)) | always19(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s84, s85)) | (~always19(s84)) | always19(s85))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8717,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s84, s85)) | (~always19(s84)) | always19(s85))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8718,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s84, s85)) | (~always19(s84)) | always19(s85)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8717, 8716])).
% 1.61/1.55 tff(8719,plain,
% 1.61/1.55 ((~always19(s84)) | always19(s85)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8718, 8567, 7108])).
% 1.61/1.55 tff(8720,plain,
% 1.61/1.55 (~always19(s84)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8719, 8711])).
% 1.61/1.55 tff(8721,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s84) | (~node20(s84)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s84) | (~node20(s84)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8722,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s84) | (~node20(s84)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8723,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s84) | (~node20(s84))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8722, 8721])).
% 1.61/1.55 tff(8724,plain,
% 1.61/1.55 (~node20(s84)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8723, 8579, 8720])).
% 1.61/1.55 tff(8725,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state1(s83, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s83, c_n1)) | (~m_main_v_state1(s83, c_t1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8726,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s83, c_n1)) | (~m_main_v_state1(s83, c_t1)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8727,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s83, c_n1)) | (~m_main_v_state1(s83, c_t1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8726, 8725])).
% 1.61/1.55 tff(8728,plain,
% 1.61/1.55 (~m_main_v_state1(s83, c_t1)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8727, 17, 7036])).
% 1.61/1.55 tff(8729,plain,
% 1.61/1.55 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s83, c_t1) | (~node20(s83)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s83, c_t1) | (~node20(s83)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8730,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s83, c_t1) | (~node20(s83)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8731,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s83, c_t1) | (~node20(s83))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8730, 8729])).
% 1.61/1.55 tff(8732,plain,
% 1.61/1.55 (~node20(s83)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8731, 8546, 8728])).
% 1.61/1.55 tff(8733,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s82)) | (~m_main_v_state1(s82, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s82)) | (~m_main_v_state1(s82, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8734,plain,
% 1.61/1.55 (((~m_main_v_state1(s82, c_c1)) | (~always19(s82))) <=> ((~always19(s82)) | (~m_main_v_state1(s82, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8735,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s82, c_c1)) | (~always19(s82)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s82)) | (~m_main_v_state1(s82, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8734])).
% 1.61/1.55 tff(8736,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s82, c_c1)) | (~always19(s82)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s82)) | (~m_main_v_state1(s82, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8735, 8733])).
% 1.61/1.55 tff(8737,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s82, c_c1)) | (~always19(s82)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8738,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s82)) | (~m_main_v_state1(s82, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 1.61/1.55 tff(8739,plain,
% 1.61/1.55 (~always19(s82)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8738, 3439, 6954])).
% 1.61/1.55 tff(8740,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s81, s82)) | (~always19(s81)) | always19(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s81, s82)) | (~always19(s81)) | always19(s82))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8741,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s81, s82)) | (~always19(s81)) | always19(s82))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8742,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s81, s82)) | (~always19(s81)) | always19(s82)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8741, 8740])).
% 1.61/1.55 tff(8743,plain,
% 1.61/1.55 ((~always19(s81)) | always19(s82)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8742, 8567, 6870])).
% 1.61/1.55 tff(8744,plain,
% 1.61/1.55 (~always19(s81)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8743, 8739])).
% 1.61/1.55 tff(8745,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s81) | (~node20(s81)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s81) | (~node20(s81)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8746,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s81) | (~node20(s81)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8747,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s81) | (~node20(s81))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8746, 8745])).
% 1.61/1.55 tff(8748,plain,
% 1.61/1.55 (~node20(s81)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8747, 8579, 8744])).
% 1.61/1.55 tff(8749,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s80, s81)) | (~always19(s80)) | always19(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s80, s81)) | (~always19(s80)) | always19(s81))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8750,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s80, s81)) | (~always19(s80)) | always19(s81))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8751,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s80, s81)) | (~always19(s80)) | always19(s81)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8750, 8749])).
% 1.61/1.55 tff(8752,plain,
% 1.61/1.55 ((~always19(s80)) | always19(s81)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8751, 8567, 6803])).
% 1.61/1.55 tff(8753,plain,
% 1.61/1.55 (~always19(s80)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8752, 8744])).
% 1.61/1.55 tff(8754,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s80) | (~node20(s80)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s80) | (~node20(s80)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8755,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s80) | (~node20(s80)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8756,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s80) | (~node20(s80))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8755, 8754])).
% 1.61/1.55 tff(8757,plain,
% 1.61/1.55 (~node20(s80)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8756, 8579, 8753])).
% 1.61/1.55 tff(8758,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state1(s79, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s79, c_n1)) | (~m_main_v_state1(s79, c_t1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8759,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s79, c_n1)) | (~m_main_v_state1(s79, c_t1)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8760,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s79, c_n1)) | (~m_main_v_state1(s79, c_t1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8759, 8758])).
% 1.61/1.55 tff(8761,plain,
% 1.61/1.55 (~m_main_v_state1(s79, c_t1)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8760, 17, 6651])).
% 1.61/1.55 tff(8762,plain,
% 1.61/1.55 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s79, c_t1) | (~node20(s79)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s79, c_t1) | (~node20(s79)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8763,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s79, c_t1) | (~node20(s79)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8764,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s79, c_t1) | (~node20(s79))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8763, 8762])).
% 1.61/1.55 tff(8765,plain,
% 1.61/1.55 (~node20(s79)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8764, 8546, 8761])).
% 1.61/1.55 tff(8766,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s78)) | (~m_main_v_state1(s78, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s78)) | (~m_main_v_state1(s78, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8767,plain,
% 1.61/1.55 (((~m_main_v_state1(s78, c_c1)) | (~always19(s78))) <=> ((~always19(s78)) | (~m_main_v_state1(s78, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8768,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s78, c_c1)) | (~always19(s78)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s78)) | (~m_main_v_state1(s78, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8767])).
% 1.61/1.55 tff(8769,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s78, c_c1)) | (~always19(s78)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s78)) | (~m_main_v_state1(s78, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8768, 8766])).
% 1.61/1.55 tff(8770,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s78, c_c1)) | (~always19(s78)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8771,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s78)) | (~m_main_v_state1(s78, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8770, 8769])).
% 1.61/1.55 tff(8772,plain,
% 1.61/1.55 (~always19(s78)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8771, 3439, 6587])).
% 1.61/1.55 tff(8773,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s77, s78)) | (~always19(s77)) | always19(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s77, s78)) | (~always19(s77)) | always19(s78))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8774,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s77, s78)) | (~always19(s77)) | always19(s78))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8775,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s77, s78)) | (~always19(s77)) | always19(s78)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8774, 8773])).
% 1.61/1.55 tff(8776,plain,
% 1.61/1.55 ((~always19(s77)) | always19(s78)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8775, 8567, 6575])).
% 1.61/1.55 tff(8777,plain,
% 1.61/1.55 (~always19(s77)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8776, 8772])).
% 1.61/1.55 tff(8778,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s77) | (~node20(s77)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s77) | (~node20(s77)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8779,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s77) | (~node20(s77)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8780,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s77) | (~node20(s77))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8779, 8778])).
% 1.61/1.55 tff(8781,plain,
% 1.61/1.55 (~node20(s77)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8780, 8579, 8777])).
% 1.61/1.55 tff(8782,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s76, s77)) | (~always19(s76)) | always19(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s76, s77)) | (~always19(s76)) | always19(s77))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8783,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s76, s77)) | (~always19(s76)) | always19(s77))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8784,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s76, s77)) | (~always19(s76)) | always19(s77)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8783, 8782])).
% 1.61/1.55 tff(8785,plain,
% 1.61/1.55 ((~always19(s76)) | always19(s77)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8784, 8567, 6480])).
% 1.61/1.55 tff(8786,plain,
% 1.61/1.55 (~always19(s76)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8785, 8777])).
% 1.61/1.55 tff(8787,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s76) | (~node20(s76)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s76) | (~node20(s76)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8788,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s76) | (~node20(s76)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8789,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s76) | (~node20(s76))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8788, 8787])).
% 1.61/1.55 tff(8790,plain,
% 1.61/1.55 (~node20(s76)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8789, 8579, 8786])).
% 1.61/1.55 tff(8791,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state1(s75, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s75, c_n1)) | (~m_main_v_state1(s75, c_t1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8792,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s75, c_n1)) | (~m_main_v_state1(s75, c_t1)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8793,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s75, c_n1)) | (~m_main_v_state1(s75, c_t1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8792, 8791])).
% 1.61/1.55 tff(8794,plain,
% 1.61/1.55 (~m_main_v_state1(s75, c_t1)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8793, 17, 6408])).
% 1.61/1.55 tff(8795,plain,
% 1.61/1.55 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s75, c_t1) | (~node20(s75)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s75, c_t1) | (~node20(s75)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8796,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s75, c_t1) | (~node20(s75)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8797,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s75, c_t1) | (~node20(s75))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 1.61/1.55 tff(8798,plain,
% 1.61/1.55 (~node20(s75)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8797, 8546, 8794])).
% 1.61/1.55 tff(8799,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s74)) | (~m_main_v_state1(s74, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s74)) | (~m_main_v_state1(s74, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8800,plain,
% 1.61/1.55 (((~m_main_v_state1(s74, c_c1)) | (~always19(s74))) <=> ((~always19(s74)) | (~m_main_v_state1(s74, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8801,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s74, c_c1)) | (~always19(s74)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s74)) | (~m_main_v_state1(s74, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8800])).
% 1.61/1.55 tff(8802,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s74, c_c1)) | (~always19(s74)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s74)) | (~m_main_v_state1(s74, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8801, 8799])).
% 1.61/1.55 tff(8803,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s74, c_c1)) | (~always19(s74)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8804,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s74)) | (~m_main_v_state1(s74, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8803, 8802])).
% 1.61/1.55 tff(8805,plain,
% 1.61/1.55 (~always19(s74)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8804, 3439, 6326])).
% 1.61/1.55 tff(8806,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s73, s74)) | (~always19(s73)) | always19(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s73, s74)) | (~always19(s73)) | always19(s74))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8807,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s73, s74)) | (~always19(s73)) | always19(s74))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8808,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s73, s74)) | (~always19(s73)) | always19(s74)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8807, 8806])).
% 1.61/1.55 tff(8809,plain,
% 1.61/1.55 ((~always19(s73)) | always19(s74)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8808, 8567, 6242])).
% 1.61/1.55 tff(8810,plain,
% 1.61/1.55 (~always19(s73)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8809, 8805])).
% 1.61/1.55 tff(8811,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s73) | (~node20(s73)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s73) | (~node20(s73)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8812,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s73) | (~node20(s73)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8813,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s73) | (~node20(s73))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8812, 8811])).
% 1.61/1.55 tff(8814,plain,
% 1.61/1.55 (~node20(s73)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8813, 8579, 8810])).
% 1.61/1.55 tff(8815,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s72, s73)) | (~always19(s72)) | always19(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s72, s73)) | (~always19(s72)) | always19(s73))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8816,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s72, s73)) | (~always19(s72)) | always19(s73))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8817,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s72, s73)) | (~always19(s72)) | always19(s73)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8816, 8815])).
% 1.61/1.55 tff(8818,plain,
% 1.61/1.55 ((~always19(s72)) | always19(s73)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8817, 8567, 6175])).
% 1.61/1.55 tff(8819,plain,
% 1.61/1.55 (~always19(s72)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8818, 8810])).
% 1.61/1.55 tff(8820,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s72) | (~node20(s72)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s72) | (~node20(s72)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8821,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s72) | (~node20(s72)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8822,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s72) | (~node20(s72))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8821, 8820])).
% 1.61/1.55 tff(8823,plain,
% 1.61/1.55 (~node20(s72)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8822, 8579, 8819])).
% 1.61/1.55 tff(8824,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state1(s71, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s71, c_n1)) | (~m_main_v_state1(s71, c_t1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8825,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s71, c_n1)) | (~m_main_v_state1(s71, c_t1)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8826,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s71, c_n1)) | (~m_main_v_state1(s71, c_t1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8825, 8824])).
% 1.61/1.55 tff(8827,plain,
% 1.61/1.55 (~m_main_v_state1(s71, c_t1)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8826, 17, 6023])).
% 1.61/1.55 tff(8828,plain,
% 1.61/1.55 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s71, c_t1) | (~node20(s71)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s71, c_t1) | (~node20(s71)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8829,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s71, c_t1) | (~node20(s71)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8830,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s71, c_t1) | (~node20(s71))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8829, 8828])).
% 1.61/1.55 tff(8831,plain,
% 1.61/1.55 (~node20(s71)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8830, 8546, 8827])).
% 1.61/1.55 tff(8832,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s70)) | (~m_main_v_state1(s70, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s70)) | (~m_main_v_state1(s70, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8833,plain,
% 1.61/1.55 (((~m_main_v_state1(s70, c_c1)) | (~always19(s70))) <=> ((~always19(s70)) | (~m_main_v_state1(s70, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8834,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s70, c_c1)) | (~always19(s70)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s70)) | (~m_main_v_state1(s70, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8833])).
% 1.61/1.55 tff(8835,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s70, c_c1)) | (~always19(s70)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s70)) | (~m_main_v_state1(s70, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8834, 8832])).
% 1.61/1.55 tff(8836,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s70, c_c1)) | (~always19(s70)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8837,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s70)) | (~m_main_v_state1(s70, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8836, 8835])).
% 1.61/1.55 tff(8838,plain,
% 1.61/1.55 (~always19(s70)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8837, 3439, 5959])).
% 1.61/1.55 tff(8839,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s69, s70)) | (~always19(s69)) | always19(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s69, s70)) | (~always19(s69)) | always19(s70))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8840,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s69, s70)) | (~always19(s69)) | always19(s70))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8841,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s69, s70)) | (~always19(s69)) | always19(s70)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8840, 8839])).
% 1.61/1.55 tff(8842,plain,
% 1.61/1.55 ((~always19(s69)) | always19(s70)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8841, 8567, 5947])).
% 1.61/1.55 tff(8843,plain,
% 1.61/1.55 (~always19(s69)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8842, 8838])).
% 1.61/1.55 tff(8844,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s69) | (~node20(s69)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s69) | (~node20(s69)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8845,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s69) | (~node20(s69)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8846,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s69) | (~node20(s69))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8845, 8844])).
% 1.61/1.55 tff(8847,plain,
% 1.61/1.55 (~node20(s69)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8846, 8579, 8843])).
% 1.61/1.55 tff(8848,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s68, s69)) | (~always19(s68)) | always19(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s68, s69)) | (~always19(s68)) | always19(s69))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8849,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s68, s69)) | (~always19(s68)) | always19(s69))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8850,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s68, s69)) | (~always19(s68)) | always19(s69)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8849, 8848])).
% 1.61/1.55 tff(8851,plain,
% 1.61/1.55 ((~always19(s68)) | always19(s69)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8850, 8567, 5852])).
% 1.61/1.55 tff(8852,plain,
% 1.61/1.55 (~always19(s68)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8851, 8843])).
% 1.61/1.55 tff(8853,plain,
% 1.61/1.55 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s68) | (~node20(s68)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s68) | (~node20(s68)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8854,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s68) | (~node20(s68)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8855,plain,
% 1.61/1.55 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s68) | (~node20(s68))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8854, 8853])).
% 1.61/1.55 tff(8856,plain,
% 1.61/1.55 (~node20(s68)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8855, 8579, 8852])).
% 1.61/1.55 tff(8857,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state1(s67, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s67, c_n1)) | (~m_main_v_state1(s67, c_t1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8858,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s67, c_n1)) | (~m_main_v_state1(s67, c_t1)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8859,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s67, c_n1)) | (~m_main_v_state1(s67, c_t1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8858, 8857])).
% 1.61/1.55 tff(8860,plain,
% 1.61/1.55 (~m_main_v_state1(s67, c_t1)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8859, 17, 5780])).
% 1.61/1.55 tff(8861,plain,
% 1.61/1.55 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s67, c_t1) | (~node20(s67)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s67, c_t1) | (~node20(s67)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8862,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s67, c_t1) | (~node20(s67)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8863,plain,
% 1.61/1.55 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s67, c_t1) | (~node20(s67))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8862, 8861])).
% 1.61/1.55 tff(8864,plain,
% 1.61/1.55 (~node20(s67)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8863, 8546, 8860])).
% 1.61/1.55 tff(8865,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s66)) | (~m_main_v_state1(s66, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s66)) | (~m_main_v_state1(s66, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8866,plain,
% 1.61/1.55 (((~m_main_v_state1(s66, c_c1)) | (~always19(s66))) <=> ((~always19(s66)) | (~m_main_v_state1(s66, c_c1)))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8867,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s66, c_c1)) | (~always19(s66)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s66)) | (~m_main_v_state1(s66, c_c1))))),
% 1.61/1.55 inference(monotonicity,[status(thm)],[8866])).
% 1.61/1.55 tff(8868,plain,
% 1.61/1.55 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s66, c_c1)) | (~always19(s66)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s66)) | (~m_main_v_state1(s66, c_c1)))),
% 1.61/1.55 inference(transitivity,[status(thm)],[8867, 8865])).
% 1.61/1.55 tff(8869,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s66, c_c1)) | (~always19(s66)))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8870,plain,
% 1.61/1.55 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s66)) | (~m_main_v_state1(s66, c_c1))),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8869, 8868])).
% 1.61/1.55 tff(8871,plain,
% 1.61/1.55 (~always19(s66)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8870, 3439, 5698])).
% 1.61/1.55 tff(8872,plain,
% 1.61/1.55 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s65, s66)) | (~always19(s65)) | always19(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s65, s66)) | (~always19(s65)) | always19(s66))),
% 1.61/1.55 inference(rewrite,[status(thm)],[])).
% 1.61/1.55 tff(8873,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s65, s66)) | (~always19(s65)) | always19(s66))),
% 1.61/1.55 inference(quant_inst,[status(thm)],[])).
% 1.61/1.55 tff(8874,plain,
% 1.61/1.55 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s65, s66)) | (~always19(s65)) | always19(s66)),
% 1.61/1.55 inference(modus_ponens,[status(thm)],[8873, 8872])).
% 1.61/1.55 tff(8875,plain,
% 1.61/1.55 ((~always19(s65)) | always19(s66)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8874, 8567, 5614])).
% 1.61/1.55 tff(8876,plain,
% 1.61/1.55 (~always19(s65)),
% 1.61/1.55 inference(unit_resolution,[status(thm)],[8875, 8871])).
% 1.61/1.56 tff(8877,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s65) | (~node20(s65)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s65) | (~node20(s65)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8878,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s65) | (~node20(s65)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8879,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s65) | (~node20(s65))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8878, 8877])).
% 1.61/1.56 tff(8880,plain,
% 1.61/1.56 (~node20(s65)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8879, 8579, 8876])).
% 1.61/1.56 tff(8881,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s64, s65)) | (~always19(s64)) | always19(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s64, s65)) | (~always19(s64)) | always19(s65))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8882,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s64, s65)) | (~always19(s64)) | always19(s65))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8883,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s64, s65)) | (~always19(s64)) | always19(s65)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8882, 8881])).
% 1.61/1.56 tff(8884,plain,
% 1.61/1.56 ((~always19(s64)) | always19(s65)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8883, 8567, 5547])).
% 1.61/1.56 tff(8885,plain,
% 1.61/1.56 (~always19(s64)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8884, 8876])).
% 1.61/1.56 tff(8886,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s64) | (~node20(s64)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s64) | (~node20(s64)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8887,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s64) | (~node20(s64)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8888,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s64) | (~node20(s64))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8887, 8886])).
% 1.61/1.56 tff(8889,plain,
% 1.61/1.56 (~node20(s64)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8888, 8579, 8885])).
% 1.61/1.56 tff(8890,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state1(s63, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s63, c_n1)) | (~m_main_v_state1(s63, c_t1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8891,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s63, c_n1)) | (~m_main_v_state1(s63, c_t1)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8892,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s63, c_n1)) | (~m_main_v_state1(s63, c_t1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8891, 8890])).
% 1.61/1.56 tff(8893,plain,
% 1.61/1.56 (~m_main_v_state1(s63, c_t1)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8892, 17, 5395])).
% 1.61/1.56 tff(8894,plain,
% 1.61/1.56 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s63, c_t1) | (~node20(s63)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s63, c_t1) | (~node20(s63)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8895,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s63, c_t1) | (~node20(s63)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8896,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s63, c_t1) | (~node20(s63))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8895, 8894])).
% 1.61/1.56 tff(8897,plain,
% 1.61/1.56 (~node20(s63)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8896, 8546, 8893])).
% 1.61/1.56 tff(8898,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s62)) | (~m_main_v_state1(s62, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s62)) | (~m_main_v_state1(s62, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8899,plain,
% 1.61/1.56 (((~m_main_v_state1(s62, c_c1)) | (~always19(s62))) <=> ((~always19(s62)) | (~m_main_v_state1(s62, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8900,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s62, c_c1)) | (~always19(s62)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s62)) | (~m_main_v_state1(s62, c_c1))))),
% 1.61/1.56 inference(monotonicity,[status(thm)],[8899])).
% 1.61/1.56 tff(8901,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s62, c_c1)) | (~always19(s62)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s62)) | (~m_main_v_state1(s62, c_c1)))),
% 1.61/1.56 inference(transitivity,[status(thm)],[8900, 8898])).
% 1.61/1.56 tff(8902,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s62, c_c1)) | (~always19(s62)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8903,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s62)) | (~m_main_v_state1(s62, c_c1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8902, 8901])).
% 1.61/1.56 tff(8904,plain,
% 1.61/1.56 (~always19(s62)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8903, 3439, 5331])).
% 1.61/1.56 tff(8905,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s61, s62)) | (~always19(s61)) | always19(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s61, s62)) | (~always19(s61)) | always19(s62))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8906,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s61, s62)) | (~always19(s61)) | always19(s62))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8907,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s61, s62)) | (~always19(s61)) | always19(s62)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8906, 8905])).
% 1.61/1.56 tff(8908,plain,
% 1.61/1.56 ((~always19(s61)) | always19(s62)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8907, 8567, 5319])).
% 1.61/1.56 tff(8909,plain,
% 1.61/1.56 (~always19(s61)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8908, 8904])).
% 1.61/1.56 tff(8910,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s61) | (~node20(s61)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s61) | (~node20(s61)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8911,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s61) | (~node20(s61)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8912,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s61) | (~node20(s61))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8911, 8910])).
% 1.61/1.56 tff(8913,plain,
% 1.61/1.56 (~node20(s61)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8912, 8579, 8909])).
% 1.61/1.56 tff(8914,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s60, s61)) | (~always19(s60)) | always19(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s60, s61)) | (~always19(s60)) | always19(s61))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8915,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s60, s61)) | (~always19(s60)) | always19(s61))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8916,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s60, s61)) | (~always19(s60)) | always19(s61)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8915, 8914])).
% 1.61/1.56 tff(8917,plain,
% 1.61/1.56 ((~always19(s60)) | always19(s61)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8916, 8567, 5224])).
% 1.61/1.56 tff(8918,plain,
% 1.61/1.56 (~always19(s60)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8917, 8909])).
% 1.61/1.56 tff(8919,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s60) | (~node20(s60)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s60) | (~node20(s60)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8920,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s60) | (~node20(s60)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8921,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s60) | (~node20(s60))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 1.61/1.56 tff(8922,plain,
% 1.61/1.56 (~node20(s60)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8921, 8579, 8918])).
% 1.61/1.56 tff(8923,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state1(s59, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state1(s59, c_t1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8924,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s59, c_n1)) | (~m_main_v_state1(s59, c_t1)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8925,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s59, c_n1)) | (~m_main_v_state1(s59, c_t1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8924, 8923])).
% 1.61/1.56 tff(8926,plain,
% 1.61/1.56 (~m_main_v_state1(s59, c_t1)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8925, 17, 5152])).
% 1.61/1.56 tff(8927,plain,
% 1.61/1.56 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s59, c_t1) | (~node20(s59)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s59, c_t1) | (~node20(s59)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8928,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s59, c_t1) | (~node20(s59)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8929,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s59, c_t1) | (~node20(s59))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8928, 8927])).
% 1.61/1.56 tff(8930,plain,
% 1.61/1.56 (~node20(s59)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8929, 8546, 8926])).
% 1.61/1.56 tff(8931,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s58)) | (~m_main_v_state1(s58, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s58)) | (~m_main_v_state1(s58, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8932,plain,
% 1.61/1.56 (((~m_main_v_state1(s58, c_c1)) | (~always19(s58))) <=> ((~always19(s58)) | (~m_main_v_state1(s58, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8933,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s58, c_c1)) | (~always19(s58)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s58)) | (~m_main_v_state1(s58, c_c1))))),
% 1.61/1.56 inference(monotonicity,[status(thm)],[8932])).
% 1.61/1.56 tff(8934,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s58, c_c1)) | (~always19(s58)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s58)) | (~m_main_v_state1(s58, c_c1)))),
% 1.61/1.56 inference(transitivity,[status(thm)],[8933, 8931])).
% 1.61/1.56 tff(8935,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s58, c_c1)) | (~always19(s58)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8936,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s58)) | (~m_main_v_state1(s58, c_c1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8935, 8934])).
% 1.61/1.56 tff(8937,plain,
% 1.61/1.56 (~always19(s58)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8936, 3439, 5070])).
% 1.61/1.56 tff(8938,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s57, s58)) | (~always19(s57)) | always19(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s57, s58)) | (~always19(s57)) | always19(s58))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8939,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s57, s58)) | (~always19(s57)) | always19(s58))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8940,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s57, s58)) | (~always19(s57)) | always19(s58)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8939, 8938])).
% 1.61/1.56 tff(8941,plain,
% 1.61/1.56 ((~always19(s57)) | always19(s58)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8940, 8567, 4986])).
% 1.61/1.56 tff(8942,plain,
% 1.61/1.56 (~always19(s57)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8941, 8937])).
% 1.61/1.56 tff(8943,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s57) | (~node20(s57)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s57) | (~node20(s57)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8944,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s57) | (~node20(s57)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8945,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s57) | (~node20(s57))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8944, 8943])).
% 1.61/1.56 tff(8946,plain,
% 1.61/1.56 (~node20(s57)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8945, 8579, 8942])).
% 1.61/1.56 tff(8947,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s56, s57)) | (~always19(s56)) | always19(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s56, s57)) | (~always19(s56)) | always19(s57))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8948,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s56, s57)) | (~always19(s56)) | always19(s57))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8949,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s56, s57)) | (~always19(s56)) | always19(s57)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8948, 8947])).
% 1.61/1.56 tff(8950,plain,
% 1.61/1.56 ((~always19(s56)) | always19(s57)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8949, 8567, 4919])).
% 1.61/1.56 tff(8951,plain,
% 1.61/1.56 (~always19(s56)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8950, 8942])).
% 1.61/1.56 tff(8952,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s56) | (~node20(s56)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s56) | (~node20(s56)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8953,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s56) | (~node20(s56)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8954,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s56) | (~node20(s56))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8953, 8952])).
% 1.61/1.56 tff(8955,plain,
% 1.61/1.56 (~node20(s56)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8954, 8579, 8951])).
% 1.61/1.56 tff(8956,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state1(s55, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state1(s55, c_t1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8957,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s55, c_n1)) | (~m_main_v_state1(s55, c_t1)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8958,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s55, c_n1)) | (~m_main_v_state1(s55, c_t1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8957, 8956])).
% 1.61/1.56 tff(8959,plain,
% 1.61/1.56 (~m_main_v_state1(s55, c_t1)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8958, 17, 4767])).
% 1.61/1.56 tff(8960,plain,
% 1.61/1.56 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s55, c_t1) | (~node20(s55)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s55, c_t1) | (~node20(s55)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8961,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s55, c_t1) | (~node20(s55)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8962,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s55, c_t1) | (~node20(s55))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8961, 8960])).
% 1.61/1.56 tff(8963,plain,
% 1.61/1.56 (~node20(s55)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8962, 8546, 8959])).
% 1.61/1.56 tff(8964,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s54)) | (~m_main_v_state1(s54, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s54)) | (~m_main_v_state1(s54, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8965,plain,
% 1.61/1.56 (((~m_main_v_state1(s54, c_c1)) | (~always19(s54))) <=> ((~always19(s54)) | (~m_main_v_state1(s54, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8966,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s54, c_c1)) | (~always19(s54)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s54)) | (~m_main_v_state1(s54, c_c1))))),
% 1.61/1.56 inference(monotonicity,[status(thm)],[8965])).
% 1.61/1.56 tff(8967,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s54, c_c1)) | (~always19(s54)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s54)) | (~m_main_v_state1(s54, c_c1)))),
% 1.61/1.56 inference(transitivity,[status(thm)],[8966, 8964])).
% 1.61/1.56 tff(8968,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s54, c_c1)) | (~always19(s54)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8969,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s54)) | (~m_main_v_state1(s54, c_c1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8968, 8967])).
% 1.61/1.56 tff(8970,plain,
% 1.61/1.56 (~always19(s54)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8969, 3439, 4703])).
% 1.61/1.56 tff(8971,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s53, s54)) | (~always19(s53)) | always19(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s53, s54)) | (~always19(s53)) | always19(s54))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8972,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s53, s54)) | (~always19(s53)) | always19(s54))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8973,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s53, s54)) | (~always19(s53)) | always19(s54)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8972, 8971])).
% 1.61/1.56 tff(8974,plain,
% 1.61/1.56 ((~always19(s53)) | always19(s54)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8973, 8567, 4691])).
% 1.61/1.56 tff(8975,plain,
% 1.61/1.56 (~always19(s53)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8974, 8970])).
% 1.61/1.56 tff(8976,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s53) | (~node20(s53)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s53) | (~node20(s53)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8977,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s53) | (~node20(s53)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8978,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s53) | (~node20(s53))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8977, 8976])).
% 1.61/1.56 tff(8979,plain,
% 1.61/1.56 (~node20(s53)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8978, 8579, 8975])).
% 1.61/1.56 tff(8980,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s52, s53)) | (~always19(s52)) | always19(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s52, s53)) | (~always19(s52)) | always19(s53))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8981,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s52, s53)) | (~always19(s52)) | always19(s53))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8982,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s52, s53)) | (~always19(s52)) | always19(s53)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8981, 8980])).
% 1.61/1.56 tff(8983,plain,
% 1.61/1.56 ((~always19(s52)) | always19(s53)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8982, 8567, 4596])).
% 1.61/1.56 tff(8984,plain,
% 1.61/1.56 (~always19(s52)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8983, 8975])).
% 1.61/1.56 tff(8985,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s52) | (~node20(s52)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s52) | (~node20(s52)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8986,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s52) | (~node20(s52)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8987,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s52) | (~node20(s52))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8986, 8985])).
% 1.61/1.56 tff(8988,plain,
% 1.61/1.56 (~node20(s52)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8987, 8579, 8984])).
% 1.61/1.56 tff(8989,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state1(s51, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state1(s51, c_t1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8990,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s51, c_n1)) | (~m_main_v_state1(s51, c_t1)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8991,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s51, c_n1)) | (~m_main_v_state1(s51, c_t1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8990, 8989])).
% 1.61/1.56 tff(8992,plain,
% 1.61/1.56 (~m_main_v_state1(s51, c_t1)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8991, 17, 4524])).
% 1.61/1.56 tff(8993,plain,
% 1.61/1.56 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s51, c_t1) | (~node20(s51)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s51, c_t1) | (~node20(s51)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8994,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s51, c_t1) | (~node20(s51)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(8995,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s51, c_t1) | (~node20(s51))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[8994, 8993])).
% 1.61/1.56 tff(8996,plain,
% 1.61/1.56 (~node20(s51)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[8995, 8546, 8992])).
% 1.61/1.56 tff(8997,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s50)) | (~m_main_v_state1(s50, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s50)) | (~m_main_v_state1(s50, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8998,plain,
% 1.61/1.56 (((~m_main_v_state1(s50, c_c1)) | (~always19(s50))) <=> ((~always19(s50)) | (~m_main_v_state1(s50, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(8999,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s50, c_c1)) | (~always19(s50)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s50)) | (~m_main_v_state1(s50, c_c1))))),
% 1.61/1.56 inference(monotonicity,[status(thm)],[8998])).
% 1.61/1.56 tff(9000,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s50, c_c1)) | (~always19(s50)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s50)) | (~m_main_v_state1(s50, c_c1)))),
% 1.61/1.56 inference(transitivity,[status(thm)],[8999, 8997])).
% 1.61/1.56 tff(9001,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s50, c_c1)) | (~always19(s50)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9002,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s50)) | (~m_main_v_state1(s50, c_c1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9001, 9000])).
% 1.61/1.56 tff(9003,plain,
% 1.61/1.56 (~always19(s50)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9002, 3439, 4442])).
% 1.61/1.56 tff(9004,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s49, s50)) | (~always19(s49)) | always19(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s49, s50)) | (~always19(s49)) | always19(s50))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9005,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s49, s50)) | (~always19(s49)) | always19(s50))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9006,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s49, s50)) | (~always19(s49)) | always19(s50)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9005, 9004])).
% 1.61/1.56 tff(9007,plain,
% 1.61/1.56 ((~always19(s49)) | always19(s50)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9006, 8567, 4358])).
% 1.61/1.56 tff(9008,plain,
% 1.61/1.56 (~always19(s49)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9007, 9003])).
% 1.61/1.56 tff(9009,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s49) | (~node20(s49)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s49) | (~node20(s49)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9010,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s49) | (~node20(s49)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9011,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s49) | (~node20(s49))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9010, 9009])).
% 1.61/1.56 tff(9012,plain,
% 1.61/1.56 (~node20(s49)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9011, 8579, 9008])).
% 1.61/1.56 tff(9013,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s48, s49)) | (~always19(s48)) | always19(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s48, s49)) | (~always19(s48)) | always19(s49))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9014,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s48, s49)) | (~always19(s48)) | always19(s49))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9015,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s48, s49)) | (~always19(s48)) | always19(s49)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9014, 9013])).
% 1.61/1.56 tff(9016,plain,
% 1.61/1.56 ((~always19(s48)) | always19(s49)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9015, 8567, 4291])).
% 1.61/1.56 tff(9017,plain,
% 1.61/1.56 (~always19(s48)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9016, 9008])).
% 1.61/1.56 tff(9018,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s48) | (~node20(s48)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s48) | (~node20(s48)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9019,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s48) | (~node20(s48)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9020,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s48) | (~node20(s48))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9019, 9018])).
% 1.61/1.56 tff(9021,plain,
% 1.61/1.56 (~node20(s48)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9020, 8579, 9017])).
% 1.61/1.56 tff(9022,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state1(s47, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state1(s47, c_t1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9023,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s47, c_n1)) | (~m_main_v_state1(s47, c_t1)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9024,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s47, c_n1)) | (~m_main_v_state1(s47, c_t1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9023, 9022])).
% 1.61/1.56 tff(9025,plain,
% 1.61/1.56 (~m_main_v_state1(s47, c_t1)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9024, 17, 4139])).
% 1.61/1.56 tff(9026,plain,
% 1.61/1.56 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s47, c_t1) | (~node20(s47)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s47, c_t1) | (~node20(s47)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9027,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s47, c_t1) | (~node20(s47)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9028,plain,
% 1.61/1.56 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s47, c_t1) | (~node20(s47))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9027, 9026])).
% 1.61/1.56 tff(9029,plain,
% 1.61/1.56 (~node20(s47)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9028, 8546, 9025])).
% 1.61/1.56 tff(9030,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s46)) | (~m_main_v_state1(s46, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s46)) | (~m_main_v_state1(s46, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9031,plain,
% 1.61/1.56 (((~m_main_v_state1(s46, c_c1)) | (~always19(s46))) <=> ((~always19(s46)) | (~m_main_v_state1(s46, c_c1)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9032,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s46, c_c1)) | (~always19(s46)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s46)) | (~m_main_v_state1(s46, c_c1))))),
% 1.61/1.56 inference(monotonicity,[status(thm)],[9031])).
% 1.61/1.56 tff(9033,plain,
% 1.61/1.56 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s46, c_c1)) | (~always19(s46)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s46)) | (~m_main_v_state1(s46, c_c1)))),
% 1.61/1.56 inference(transitivity,[status(thm)],[9032, 9030])).
% 1.61/1.56 tff(9034,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s46, c_c1)) | (~always19(s46)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9035,plain,
% 1.61/1.56 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s46)) | (~m_main_v_state1(s46, c_c1))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9034, 9033])).
% 1.61/1.56 tff(9036,plain,
% 1.61/1.56 (~always19(s46)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9035, 3439, 4075])).
% 1.61/1.56 tff(9037,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s45, s46)) | (~always19(s45)) | always19(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s45, s46)) | (~always19(s45)) | always19(s46))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9038,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s45, s46)) | (~always19(s45)) | always19(s46))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9039,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s45, s46)) | (~always19(s45)) | always19(s46)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9038, 9037])).
% 1.61/1.56 tff(9040,plain,
% 1.61/1.56 ((~always19(s45)) | always19(s46)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9039, 8567, 4063])).
% 1.61/1.56 tff(9041,plain,
% 1.61/1.56 (~always19(s45)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9040, 9036])).
% 1.61/1.56 tff(9042,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s45) | (~node20(s45)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s45) | (~node20(s45)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9043,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s45) | (~node20(s45)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9044,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s45) | (~node20(s45))),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9043, 9042])).
% 1.61/1.56 tff(9045,plain,
% 1.61/1.56 (~node20(s45)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9044, 8579, 9041])).
% 1.61/1.56 tff(9046,plain,
% 1.61/1.56 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s44, s45)) | (~always19(s44)) | always19(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s44, s45)) | (~always19(s44)) | always19(s45))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9047,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s44, s45)) | (~always19(s44)) | always19(s45))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9048,plain,
% 1.61/1.56 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s44, s45)) | (~always19(s44)) | always19(s45)),
% 1.61/1.56 inference(modus_ponens,[status(thm)],[9047, 9046])).
% 1.61/1.56 tff(9049,plain,
% 1.61/1.56 ((~always19(s44)) | always19(s45)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9048, 8567, 3968])).
% 1.61/1.56 tff(9050,plain,
% 1.61/1.56 (~always19(s44)),
% 1.61/1.56 inference(unit_resolution,[status(thm)],[9049, 9041])).
% 1.61/1.56 tff(9051,plain,
% 1.61/1.56 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s44) | (~node20(s44)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s44) | (~node20(s44)))),
% 1.61/1.56 inference(rewrite,[status(thm)],[])).
% 1.61/1.56 tff(9052,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s44) | (~node20(s44)))),
% 1.61/1.56 inference(quant_inst,[status(thm)],[])).
% 1.61/1.56 tff(9053,plain,
% 1.61/1.56 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s44) | (~node20(s44))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9052, 9051])).
% 1.61/1.57 tff(9054,plain,
% 1.61/1.57 (~node20(s44)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9053, 8579, 9050])).
% 1.61/1.57 tff(9055,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state1(s43, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state1(s43, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9056,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s43, c_n1)) | (~m_main_v_state1(s43, c_t1)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9057,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s43, c_n1)) | (~m_main_v_state1(s43, c_t1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9056, 9055])).
% 1.61/1.57 tff(9058,plain,
% 1.61/1.57 (~m_main_v_state1(s43, c_t1)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9057, 17, 3896])).
% 1.61/1.57 tff(9059,plain,
% 1.61/1.57 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s43, c_t1) | (~node20(s43)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s43, c_t1) | (~node20(s43)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9060,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s43, c_t1) | (~node20(s43)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9061,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s43, c_t1) | (~node20(s43))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9060, 9059])).
% 1.61/1.57 tff(9062,plain,
% 1.61/1.57 (~node20(s43)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9061, 8546, 9058])).
% 1.61/1.57 tff(9063,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s42)) | (~m_main_v_state1(s42, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s42)) | (~m_main_v_state1(s42, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9064,plain,
% 1.61/1.57 (((~m_main_v_state1(s42, c_c1)) | (~always19(s42))) <=> ((~always19(s42)) | (~m_main_v_state1(s42, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9065,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s42, c_c1)) | (~always19(s42)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s42)) | (~m_main_v_state1(s42, c_c1))))),
% 1.61/1.57 inference(monotonicity,[status(thm)],[9064])).
% 1.61/1.57 tff(9066,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s42, c_c1)) | (~always19(s42)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s42)) | (~m_main_v_state1(s42, c_c1)))),
% 1.61/1.57 inference(transitivity,[status(thm)],[9065, 9063])).
% 1.61/1.57 tff(9067,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s42, c_c1)) | (~always19(s42)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9068,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s42)) | (~m_main_v_state1(s42, c_c1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9067, 9066])).
% 1.61/1.57 tff(9069,plain,
% 1.61/1.57 (~always19(s42)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9068, 3439, 3814])).
% 1.61/1.57 tff(9070,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s41, s42)) | (~always19(s41)) | always19(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s41, s42)) | (~always19(s41)) | always19(s42))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9071,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s41, s42)) | (~always19(s41)) | always19(s42))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9072,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s41, s42)) | (~always19(s41)) | always19(s42)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 1.61/1.57 tff(9073,plain,
% 1.61/1.57 ((~always19(s41)) | always19(s42)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9072, 8567, 3730])).
% 1.61/1.57 tff(9074,plain,
% 1.61/1.57 (~always19(s41)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9073, 9069])).
% 1.61/1.57 tff(9075,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s41) | (~node20(s41)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s41) | (~node20(s41)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9076,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s41) | (~node20(s41)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9077,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s41) | (~node20(s41))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 1.61/1.57 tff(9078,plain,
% 1.61/1.57 (~node20(s41)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9077, 8579, 9074])).
% 1.61/1.57 tff(9079,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s40, s41)) | (~always19(s40)) | always19(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s40, s41)) | (~always19(s40)) | always19(s41))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9080,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s40, s41)) | (~always19(s40)) | always19(s41))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9081,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s40, s41)) | (~always19(s40)) | always19(s41)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9080, 9079])).
% 1.61/1.57 tff(9082,plain,
% 1.61/1.57 ((~always19(s40)) | always19(s41)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9081, 8567, 3663])).
% 1.61/1.57 tff(9083,plain,
% 1.61/1.57 (~always19(s40)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9082, 9074])).
% 1.61/1.57 tff(9084,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s40) | (~node20(s40)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s40) | (~node20(s40)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9085,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s40) | (~node20(s40)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9086,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s40) | (~node20(s40))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9085, 9084])).
% 1.61/1.57 tff(9087,plain,
% 1.61/1.57 (~node20(s40)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9086, 8579, 9083])).
% 1.61/1.57 tff(9088,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state1(s39, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state1(s39, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9089,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s39, c_n1)) | (~m_main_v_state1(s39, c_t1)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9090,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s39, c_n1)) | (~m_main_v_state1(s39, c_t1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9089, 9088])).
% 1.61/1.57 tff(9091,plain,
% 1.61/1.57 (~m_main_v_state1(s39, c_t1)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9090, 17, 3511])).
% 1.61/1.57 tff(9092,plain,
% 1.61/1.57 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s39, c_t1) | (~node20(s39)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s39, c_t1) | (~node20(s39)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9093,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s39, c_t1) | (~node20(s39)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9094,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s39, c_t1) | (~node20(s39))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9093, 9092])).
% 1.61/1.57 tff(9095,plain,
% 1.61/1.57 (~node20(s39)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9094, 8546, 9091])).
% 1.61/1.57 tff(9096,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s37, s38)) | (~always19(s37)) | always19(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s37, s38)) | (~always19(s37)) | always19(s38))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9097,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s37, s38)) | (~always19(s37)) | always19(s38))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9098,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s37, s38)) | (~always19(s37)) | always19(s38)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9097, 9096])).
% 1.61/1.57 tff(9099,plain,
% 1.61/1.57 ((~always19(s37)) | always19(s38)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9098, 8567, 3420])).
% 1.61/1.57 tff(9100,plain,
% 1.61/1.57 (~always19(s37)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9099, 3446])).
% 1.61/1.57 tff(9101,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s37) | (~node20(s37)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s37) | (~node20(s37)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9102,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s37) | (~node20(s37)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9103,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s37) | (~node20(s37))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9102, 9101])).
% 1.61/1.57 tff(9104,plain,
% 1.61/1.57 (~node20(s37)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9103, 8579, 9100])).
% 1.61/1.57 tff(9105,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s36, s37)) | (~always19(s36)) | always19(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s36, s37)) | (~always19(s36)) | always19(s37))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9106,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s36, s37)) | (~always19(s36)) | always19(s37))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9107,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s36, s37)) | (~always19(s36)) | always19(s37)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9106, 9105])).
% 1.61/1.57 tff(9108,plain,
% 1.61/1.57 ((~always19(s36)) | always19(s37)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9107, 8567, 3325])).
% 1.61/1.57 tff(9109,plain,
% 1.61/1.57 (~always19(s36)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9108, 9100])).
% 1.61/1.57 tff(9110,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s36) | (~node20(s36)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s36) | (~node20(s36)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9111,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s36) | (~node20(s36)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9112,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s36) | (~node20(s36))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9111, 9110])).
% 1.61/1.57 tff(9113,plain,
% 1.61/1.57 (~node20(s36)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9112, 8579, 9109])).
% 1.61/1.57 tff(9114,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state1(s35, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state1(s35, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9115,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s35, c_n1)) | (~m_main_v_state1(s35, c_t1)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9116,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s35, c_n1)) | (~m_main_v_state1(s35, c_t1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9115, 9114])).
% 1.61/1.57 tff(9117,plain,
% 1.61/1.57 (~m_main_v_state1(s35, c_t1)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9116, 17, 3253])).
% 1.61/1.57 tff(9118,plain,
% 1.61/1.57 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s35, c_t1) | (~node20(s35)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s35, c_t1) | (~node20(s35)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9119,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s35, c_t1) | (~node20(s35)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9120,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s35, c_t1) | (~node20(s35))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9119, 9118])).
% 1.61/1.57 tff(9121,plain,
% 1.61/1.57 (~node20(s35)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9120, 8546, 9117])).
% 1.61/1.57 tff(9122,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s34)) | (~m_main_v_state1(s34, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s34)) | (~m_main_v_state1(s34, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9123,plain,
% 1.61/1.57 (((~m_main_v_state1(s34, c_c1)) | (~always19(s34))) <=> ((~always19(s34)) | (~m_main_v_state1(s34, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9124,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s34, c_c1)) | (~always19(s34)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s34)) | (~m_main_v_state1(s34, c_c1))))),
% 1.61/1.57 inference(monotonicity,[status(thm)],[9123])).
% 1.61/1.57 tff(9125,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s34, c_c1)) | (~always19(s34)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s34)) | (~m_main_v_state1(s34, c_c1)))),
% 1.61/1.57 inference(transitivity,[status(thm)],[9124, 9122])).
% 1.61/1.57 tff(9126,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s34, c_c1)) | (~always19(s34)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9127,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s34)) | (~m_main_v_state1(s34, c_c1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9126, 9125])).
% 1.61/1.57 tff(9128,plain,
% 1.61/1.57 (~always19(s34)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9127, 3439, 3171])).
% 1.61/1.57 tff(9129,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s33, s34)) | (~always19(s33)) | always19(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s33, s34)) | (~always19(s33)) | always19(s34))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9130,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s33, s34)) | (~always19(s33)) | always19(s34))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9131,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s33, s34)) | (~always19(s33)) | always19(s34)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9130, 9129])).
% 1.61/1.57 tff(9132,plain,
% 1.61/1.57 ((~always19(s33)) | always19(s34)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9131, 8567, 3087])).
% 1.61/1.57 tff(9133,plain,
% 1.61/1.57 (~always19(s33)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9132, 9128])).
% 1.61/1.57 tff(9134,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s33) | (~node20(s33)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s33) | (~node20(s33)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9135,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s33) | (~node20(s33)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9136,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s33) | (~node20(s33))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 1.61/1.57 tff(9137,plain,
% 1.61/1.57 (~node20(s33)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9136, 8579, 9133])).
% 1.61/1.57 tff(9138,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s32, s33)) | (~always19(s32)) | always19(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s32, s33)) | (~always19(s32)) | always19(s33))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9139,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s32, s33)) | (~always19(s32)) | always19(s33))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9140,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s32, s33)) | (~always19(s32)) | always19(s33)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9139, 9138])).
% 1.61/1.57 tff(9141,plain,
% 1.61/1.57 ((~always19(s32)) | always19(s33)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9140, 8567, 3020])).
% 1.61/1.57 tff(9142,plain,
% 1.61/1.57 (~always19(s32)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9141, 9133])).
% 1.61/1.57 tff(9143,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s32) | (~node20(s32)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s32) | (~node20(s32)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9144,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s32) | (~node20(s32)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9145,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s32) | (~node20(s32))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9144, 9143])).
% 1.61/1.57 tff(9146,plain,
% 1.61/1.57 (~node20(s32)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9145, 8579, 9142])).
% 1.61/1.57 tff(9147,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state1(s31, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state1(s31, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9148,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s31, c_n1)) | (~m_main_v_state1(s31, c_t1)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9149,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s31, c_n1)) | (~m_main_v_state1(s31, c_t1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9148, 9147])).
% 1.61/1.57 tff(9150,plain,
% 1.61/1.57 (~m_main_v_state1(s31, c_t1)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9149, 17, 2868])).
% 1.61/1.57 tff(9151,plain,
% 1.61/1.57 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s31, c_t1) | (~node20(s31)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s31, c_t1) | (~node20(s31)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9152,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s31, c_t1) | (~node20(s31)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9153,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s31, c_t1) | (~node20(s31))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9152, 9151])).
% 1.61/1.57 tff(9154,plain,
% 1.61/1.57 (~node20(s31)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9153, 8546, 9150])).
% 1.61/1.57 tff(9155,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s30)) | (~m_main_v_state1(s30, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s30)) | (~m_main_v_state1(s30, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9156,plain,
% 1.61/1.57 (((~m_main_v_state1(s30, c_c1)) | (~always19(s30))) <=> ((~always19(s30)) | (~m_main_v_state1(s30, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9157,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s30, c_c1)) | (~always19(s30)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s30)) | (~m_main_v_state1(s30, c_c1))))),
% 1.61/1.57 inference(monotonicity,[status(thm)],[9156])).
% 1.61/1.57 tff(9158,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s30, c_c1)) | (~always19(s30)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s30)) | (~m_main_v_state1(s30, c_c1)))),
% 1.61/1.57 inference(transitivity,[status(thm)],[9157, 9155])).
% 1.61/1.57 tff(9159,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s30, c_c1)) | (~always19(s30)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9160,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s30)) | (~m_main_v_state1(s30, c_c1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9159, 9158])).
% 1.61/1.57 tff(9161,plain,
% 1.61/1.57 (~always19(s30)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9160, 3439, 2804])).
% 1.61/1.57 tff(9162,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s29, s30)) | (~always19(s29)) | always19(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s29, s30)) | (~always19(s29)) | always19(s30))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9163,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s29, s30)) | (~always19(s29)) | always19(s30))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9164,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s29, s30)) | (~always19(s29)) | always19(s30)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9163, 9162])).
% 1.61/1.57 tff(9165,plain,
% 1.61/1.57 ((~always19(s29)) | always19(s30)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9164, 8567, 2792])).
% 1.61/1.57 tff(9166,plain,
% 1.61/1.57 (~always19(s29)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9165, 9161])).
% 1.61/1.57 tff(9167,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s29) | (~node20(s29)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s29) | (~node20(s29)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9168,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s29) | (~node20(s29)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9169,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s29) | (~node20(s29))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9168, 9167])).
% 1.61/1.57 tff(9170,plain,
% 1.61/1.57 (~node20(s29)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9169, 8579, 9166])).
% 1.61/1.57 tff(9171,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s28, s29)) | (~always19(s28)) | always19(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s28, s29)) | (~always19(s28)) | always19(s29))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9172,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s28, s29)) | (~always19(s28)) | always19(s29))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9173,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s28, s29)) | (~always19(s28)) | always19(s29)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9172, 9171])).
% 1.61/1.57 tff(9174,plain,
% 1.61/1.57 ((~always19(s28)) | always19(s29)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9173, 8567, 2697])).
% 1.61/1.57 tff(9175,plain,
% 1.61/1.57 (~always19(s28)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9174, 9166])).
% 1.61/1.57 tff(9176,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s28) | (~node20(s28)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s28) | (~node20(s28)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9177,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s28) | (~node20(s28)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9178,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s28) | (~node20(s28))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9177, 9176])).
% 1.61/1.57 tff(9179,plain,
% 1.61/1.57 (~node20(s28)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9178, 8579, 9175])).
% 1.61/1.57 tff(9180,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state1(s27, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state1(s27, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9181,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s27, c_n1)) | (~m_main_v_state1(s27, c_t1)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9182,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s27, c_n1)) | (~m_main_v_state1(s27, c_t1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9181, 9180])).
% 1.61/1.57 tff(9183,plain,
% 1.61/1.57 (~m_main_v_state1(s27, c_t1)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9182, 17, 2625])).
% 1.61/1.57 tff(9184,plain,
% 1.61/1.57 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s27, c_t1) | (~node20(s27)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s27, c_t1) | (~node20(s27)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9185,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s27, c_t1) | (~node20(s27)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9186,plain,
% 1.61/1.57 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s27, c_t1) | (~node20(s27))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9185, 9184])).
% 1.61/1.57 tff(9187,plain,
% 1.61/1.57 (~node20(s27)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9186, 8546, 9183])).
% 1.61/1.57 tff(9188,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s26)) | (~m_main_v_state1(s26, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s26)) | (~m_main_v_state1(s26, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9189,plain,
% 1.61/1.57 (((~m_main_v_state1(s26, c_c1)) | (~always19(s26))) <=> ((~always19(s26)) | (~m_main_v_state1(s26, c_c1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9190,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s26, c_c1)) | (~always19(s26)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s26)) | (~m_main_v_state1(s26, c_c1))))),
% 1.61/1.57 inference(monotonicity,[status(thm)],[9189])).
% 1.61/1.57 tff(9191,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s26, c_c1)) | (~always19(s26)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s26)) | (~m_main_v_state1(s26, c_c1)))),
% 1.61/1.57 inference(transitivity,[status(thm)],[9190, 9188])).
% 1.61/1.57 tff(9192,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s26, c_c1)) | (~always19(s26)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9193,plain,
% 1.61/1.57 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s26)) | (~m_main_v_state1(s26, c_c1))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9192, 9191])).
% 1.61/1.57 tff(9194,plain,
% 1.61/1.57 (~always19(s26)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9193, 3439, 2543])).
% 1.61/1.57 tff(9195,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s25, s26)) | (~always19(s25)) | always19(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s25, s26)) | (~always19(s25)) | always19(s26))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9196,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s25, s26)) | (~always19(s25)) | always19(s26))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9197,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s25, s26)) | (~always19(s25)) | always19(s26)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9196, 9195])).
% 1.61/1.57 tff(9198,plain,
% 1.61/1.57 ((~always19(s25)) | always19(s26)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9197, 8567, 2459])).
% 1.61/1.57 tff(9199,plain,
% 1.61/1.57 (~always19(s25)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9198, 9194])).
% 1.61/1.57 tff(9200,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s25) | (~node20(s25)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s25) | (~node20(s25)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9201,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s25) | (~node20(s25)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9202,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s25) | (~node20(s25))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9201, 9200])).
% 1.61/1.57 tff(9203,plain,
% 1.61/1.57 (~node20(s25)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9202, 8579, 9199])).
% 1.61/1.57 tff(9204,plain,
% 1.61/1.57 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s24, s25)) | (~always19(s24)) | always19(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s24, s25)) | (~always19(s24)) | always19(s25))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9205,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s24, s25)) | (~always19(s24)) | always19(s25))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9206,plain,
% 1.61/1.57 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s24, s25)) | (~always19(s24)) | always19(s25)),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9205, 9204])).
% 1.61/1.57 tff(9207,plain,
% 1.61/1.57 ((~always19(s24)) | always19(s25)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9206, 8567, 2392])).
% 1.61/1.57 tff(9208,plain,
% 1.61/1.57 (~always19(s24)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9207, 9199])).
% 1.61/1.57 tff(9209,plain,
% 1.61/1.57 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s24) | (~node20(s24)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s24) | (~node20(s24)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.57 tff(9210,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s24) | (~node20(s24)))),
% 1.61/1.57 inference(quant_inst,[status(thm)],[])).
% 1.61/1.57 tff(9211,plain,
% 1.61/1.57 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s24) | (~node20(s24))),
% 1.61/1.57 inference(modus_ponens,[status(thm)],[9210, 9209])).
% 1.61/1.57 tff(9212,plain,
% 1.61/1.57 (~node20(s24)),
% 1.61/1.57 inference(unit_resolution,[status(thm)],[9211, 8579, 9208])).
% 1.61/1.57 tff(9213,plain,
% 1.61/1.57 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state1(s23, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state1(s23, c_t1)))),
% 1.61/1.57 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9214,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s23, c_n1)) | (~m_main_v_state1(s23, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9215,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s23, c_n1)) | (~m_main_v_state1(s23, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9214, 9213])).
% 1.61/1.58 tff(9216,plain,
% 1.61/1.58 (~m_main_v_state1(s23, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9215, 17, 2240])).
% 1.61/1.58 tff(9217,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s23, c_t1) | (~node20(s23)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s23, c_t1) | (~node20(s23)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9218,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s23, c_t1) | (~node20(s23)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9219,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s23, c_t1) | (~node20(s23))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9218, 9217])).
% 1.61/1.58 tff(9220,plain,
% 1.61/1.58 (~node20(s23)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9219, 8546, 9216])).
% 1.61/1.58 tff(9221,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s22)) | (~m_main_v_state1(s22, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s22)) | (~m_main_v_state1(s22, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9222,plain,
% 1.61/1.58 (((~m_main_v_state1(s22, c_c1)) | (~always19(s22))) <=> ((~always19(s22)) | (~m_main_v_state1(s22, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9223,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s22, c_c1)) | (~always19(s22)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s22)) | (~m_main_v_state1(s22, c_c1))))),
% 1.61/1.58 inference(monotonicity,[status(thm)],[9222])).
% 1.61/1.58 tff(9224,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s22, c_c1)) | (~always19(s22)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s22)) | (~m_main_v_state1(s22, c_c1)))),
% 1.61/1.58 inference(transitivity,[status(thm)],[9223, 9221])).
% 1.61/1.58 tff(9225,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s22, c_c1)) | (~always19(s22)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9226,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s22)) | (~m_main_v_state1(s22, c_c1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9225, 9224])).
% 1.61/1.58 tff(9227,plain,
% 1.61/1.58 (~always19(s22)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9226, 3439, 2176])).
% 1.61/1.58 tff(9228,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s21, s22)) | (~always19(s21)) | always19(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s21, s22)) | (~always19(s21)) | always19(s22))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9229,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s21, s22)) | (~always19(s21)) | always19(s22))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9230,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s21, s22)) | (~always19(s21)) | always19(s22)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9229, 9228])).
% 1.61/1.58 tff(9231,plain,
% 1.61/1.58 ((~always19(s21)) | always19(s22)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9230, 8567, 2164])).
% 1.61/1.58 tff(9232,plain,
% 1.61/1.58 (~always19(s21)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9231, 9227])).
% 1.61/1.58 tff(9233,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s21) | (~node20(s21)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s21) | (~node20(s21)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9234,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s21) | (~node20(s21)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9235,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s21) | (~node20(s21))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9234, 9233])).
% 1.61/1.58 tff(9236,plain,
% 1.61/1.58 (~node20(s21)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9235, 8579, 9232])).
% 1.61/1.58 tff(9237,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s20, s21)) | (~always19(s20)) | always19(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s20, s21)) | (~always19(s20)) | always19(s21))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9238,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s20, s21)) | (~always19(s20)) | always19(s21))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9239,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s20, s21)) | (~always19(s20)) | always19(s21)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9238, 9237])).
% 1.61/1.58 tff(9240,plain,
% 1.61/1.58 ((~always19(s20)) | always19(s21)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9239, 8567, 2069])).
% 1.61/1.58 tff(9241,plain,
% 1.61/1.58 (~always19(s20)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9240, 9232])).
% 1.61/1.58 tff(9242,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s20) | (~node20(s20)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s20) | (~node20(s20)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9243,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s20) | (~node20(s20)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9244,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s20) | (~node20(s20))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9243, 9242])).
% 1.61/1.58 tff(9245,plain,
% 1.61/1.58 (~node20(s20)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9244, 8579, 9241])).
% 1.61/1.58 tff(9246,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state1(s19, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state1(s19, c_t1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9247,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s19, c_n1)) | (~m_main_v_state1(s19, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9248,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s19, c_n1)) | (~m_main_v_state1(s19, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9247, 9246])).
% 1.61/1.58 tff(9249,plain,
% 1.61/1.58 (~m_main_v_state1(s19, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9248, 17, 1997])).
% 1.61/1.58 tff(9250,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s19, c_t1) | (~node20(s19)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s19, c_t1) | (~node20(s19)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9251,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s19, c_t1) | (~node20(s19)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9252,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s19, c_t1) | (~node20(s19))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9251, 9250])).
% 1.61/1.58 tff(9253,plain,
% 1.61/1.58 (~node20(s19)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9252, 8546, 9249])).
% 1.61/1.58 tff(9254,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s18)) | (~m_main_v_state1(s18, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s18)) | (~m_main_v_state1(s18, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9255,plain,
% 1.61/1.58 (((~m_main_v_state1(s18, c_c1)) | (~always19(s18))) <=> ((~always19(s18)) | (~m_main_v_state1(s18, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9256,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s18, c_c1)) | (~always19(s18)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s18)) | (~m_main_v_state1(s18, c_c1))))),
% 1.61/1.58 inference(monotonicity,[status(thm)],[9255])).
% 1.61/1.58 tff(9257,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s18, c_c1)) | (~always19(s18)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s18)) | (~m_main_v_state1(s18, c_c1)))),
% 1.61/1.58 inference(transitivity,[status(thm)],[9256, 9254])).
% 1.61/1.58 tff(9258,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s18, c_c1)) | (~always19(s18)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9259,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s18)) | (~m_main_v_state1(s18, c_c1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9258, 9257])).
% 1.61/1.58 tff(9260,plain,
% 1.61/1.58 (~always19(s18)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9259, 3439, 1915])).
% 1.61/1.58 tff(9261,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s17, s18)) | (~always19(s17)) | always19(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s17, s18)) | (~always19(s17)) | always19(s18))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9262,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s17, s18)) | (~always19(s17)) | always19(s18))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9263,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s17, s18)) | (~always19(s17)) | always19(s18)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9262, 9261])).
% 1.61/1.58 tff(9264,plain,
% 1.61/1.58 ((~always19(s17)) | always19(s18)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9263, 8567, 1831])).
% 1.61/1.58 tff(9265,plain,
% 1.61/1.58 (~always19(s17)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9264, 9260])).
% 1.61/1.58 tff(9266,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s17) | (~node20(s17)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s17) | (~node20(s17)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9267,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s17) | (~node20(s17)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9268,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s17) | (~node20(s17))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9267, 9266])).
% 1.61/1.58 tff(9269,plain,
% 1.61/1.58 (~node20(s17)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9268, 8579, 9265])).
% 1.61/1.58 tff(9270,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s16, s17)) | (~always19(s16)) | always19(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s16, s17)) | (~always19(s16)) | always19(s17))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9271,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s16, s17)) | (~always19(s16)) | always19(s17))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9272,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s16, s17)) | (~always19(s16)) | always19(s17)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 1.61/1.58 tff(9273,plain,
% 1.61/1.58 ((~always19(s16)) | always19(s17)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9272, 8567, 1764])).
% 1.61/1.58 tff(9274,plain,
% 1.61/1.58 (~always19(s16)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9273, 9265])).
% 1.61/1.58 tff(9275,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s16) | (~node20(s16)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s16) | (~node20(s16)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9276,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s16) | (~node20(s16)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9277,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s16) | (~node20(s16))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9276, 9275])).
% 1.61/1.58 tff(9278,plain,
% 1.61/1.58 (~node20(s16)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9277, 8579, 9274])).
% 1.61/1.58 tff(9279,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state1(s15, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state1(s15, c_t1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9280,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s15, c_n1)) | (~m_main_v_state1(s15, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9281,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s15, c_n1)) | (~m_main_v_state1(s15, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9280, 9279])).
% 1.61/1.58 tff(9282,plain,
% 1.61/1.58 (~m_main_v_state1(s15, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9281, 17, 1612])).
% 1.61/1.58 tff(9283,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s15, c_t1) | (~node20(s15)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s15, c_t1) | (~node20(s15)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9284,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s15, c_t1) | (~node20(s15)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9285,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s15, c_t1) | (~node20(s15))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9284, 9283])).
% 1.61/1.58 tff(9286,plain,
% 1.61/1.58 (~node20(s15)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9285, 8546, 9282])).
% 1.61/1.58 tff(9287,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s14)) | (~m_main_v_state1(s14, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s14)) | (~m_main_v_state1(s14, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9288,plain,
% 1.61/1.58 (((~m_main_v_state1(s14, c_c1)) | (~always19(s14))) <=> ((~always19(s14)) | (~m_main_v_state1(s14, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9289,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s14, c_c1)) | (~always19(s14)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s14)) | (~m_main_v_state1(s14, c_c1))))),
% 1.61/1.58 inference(monotonicity,[status(thm)],[9288])).
% 1.61/1.58 tff(9290,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s14, c_c1)) | (~always19(s14)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s14)) | (~m_main_v_state1(s14, c_c1)))),
% 1.61/1.58 inference(transitivity,[status(thm)],[9289, 9287])).
% 1.61/1.58 tff(9291,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s14, c_c1)) | (~always19(s14)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9292,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s14)) | (~m_main_v_state1(s14, c_c1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9291, 9290])).
% 1.61/1.58 tff(9293,plain,
% 1.61/1.58 (~always19(s14)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9292, 3439, 1548])).
% 1.61/1.58 tff(9294,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s13, s14)) | (~always19(s13)) | always19(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s13, s14)) | (~always19(s13)) | always19(s14))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9295,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s13, s14)) | (~always19(s13)) | always19(s14))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9296,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s13, s14)) | (~always19(s13)) | always19(s14)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9295, 9294])).
% 1.61/1.58 tff(9297,plain,
% 1.61/1.58 ((~always19(s13)) | always19(s14)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9296, 8567, 1536])).
% 1.61/1.58 tff(9298,plain,
% 1.61/1.58 (~always19(s13)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9297, 9293])).
% 1.61/1.58 tff(9299,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s13) | (~node20(s13)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s13) | (~node20(s13)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9300,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s13) | (~node20(s13)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9301,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s13) | (~node20(s13))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9300, 9299])).
% 1.61/1.58 tff(9302,plain,
% 1.61/1.58 (~node20(s13)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9301, 8579, 9298])).
% 1.61/1.58 tff(9303,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s12, s13)) | (~always19(s12)) | always19(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s12, s13)) | (~always19(s12)) | always19(s13))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9304,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s12, s13)) | (~always19(s12)) | always19(s13))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9305,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s12, s13)) | (~always19(s12)) | always19(s13)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9304, 9303])).
% 1.61/1.58 tff(9306,plain,
% 1.61/1.58 ((~always19(s12)) | always19(s13)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9305, 8567, 1441])).
% 1.61/1.58 tff(9307,plain,
% 1.61/1.58 (~always19(s12)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9306, 9298])).
% 1.61/1.58 tff(9308,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s12) | (~node20(s12)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s12) | (~node20(s12)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9309,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s12) | (~node20(s12)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9310,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s12) | (~node20(s12))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9309, 9308])).
% 1.61/1.58 tff(9311,plain,
% 1.61/1.58 (~node20(s12)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9310, 8579, 9307])).
% 1.61/1.58 tff(9312,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state1(s11, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state1(s11, c_t1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9313,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s11, c_n1)) | (~m_main_v_state1(s11, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9314,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s11, c_n1)) | (~m_main_v_state1(s11, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9313, 9312])).
% 1.61/1.58 tff(9315,plain,
% 1.61/1.58 (~m_main_v_state1(s11, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9314, 17, 1369])).
% 1.61/1.58 tff(9316,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s11, c_t1) | (~node20(s11)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s11, c_t1) | (~node20(s11)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9317,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s11, c_t1) | (~node20(s11)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9318,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s11, c_t1) | (~node20(s11))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9317, 9316])).
% 1.61/1.58 tff(9319,plain,
% 1.61/1.58 (~node20(s11)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9318, 8546, 9315])).
% 1.61/1.58 tff(9320,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s10)) | (~m_main_v_state1(s10, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s10)) | (~m_main_v_state1(s10, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9321,plain,
% 1.61/1.58 (((~m_main_v_state1(s10, c_c1)) | (~always19(s10))) <=> ((~always19(s10)) | (~m_main_v_state1(s10, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9322,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s10, c_c1)) | (~always19(s10)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s10)) | (~m_main_v_state1(s10, c_c1))))),
% 1.61/1.58 inference(monotonicity,[status(thm)],[9321])).
% 1.61/1.58 tff(9323,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s10, c_c1)) | (~always19(s10)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s10)) | (~m_main_v_state1(s10, c_c1)))),
% 1.61/1.58 inference(transitivity,[status(thm)],[9322, 9320])).
% 1.61/1.58 tff(9324,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s10, c_c1)) | (~always19(s10)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9325,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s10)) | (~m_main_v_state1(s10, c_c1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9324, 9323])).
% 1.61/1.58 tff(9326,plain,
% 1.61/1.58 (~always19(s10)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9325, 3439, 1287])).
% 1.61/1.58 tff(9327,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s9, s10)) | (~always19(s9)) | always19(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s9, s10)) | (~always19(s9)) | always19(s10))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9328,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s9, s10)) | (~always19(s9)) | always19(s10))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9329,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s9, s10)) | (~always19(s9)) | always19(s10)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 1.61/1.58 tff(9330,plain,
% 1.61/1.58 ((~always19(s9)) | always19(s10)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9329, 8567, 1203])).
% 1.61/1.58 tff(9331,plain,
% 1.61/1.58 (~always19(s9)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9330, 9326])).
% 1.61/1.58 tff(9332,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s9) | (~node20(s9)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s9) | (~node20(s9)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9333,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s9) | (~node20(s9)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9334,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s9) | (~node20(s9))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9333, 9332])).
% 1.61/1.58 tff(9335,plain,
% 1.61/1.58 (~node20(s9)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9334, 8579, 9331])).
% 1.61/1.58 tff(9336,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s8, s9)) | (~always19(s8)) | always19(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s8, s9)) | (~always19(s8)) | always19(s9))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9337,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s8, s9)) | (~always19(s8)) | always19(s9))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9338,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s8, s9)) | (~always19(s8)) | always19(s9)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9337, 9336])).
% 1.61/1.58 tff(9339,plain,
% 1.61/1.58 ((~always19(s8)) | always19(s9)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9338, 8567, 1136])).
% 1.61/1.58 tff(9340,plain,
% 1.61/1.58 (~always19(s8)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9339, 9331])).
% 1.61/1.58 tff(9341,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s8) | (~node20(s8)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s8) | (~node20(s8)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9342,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s8) | (~node20(s8)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9343,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s8) | (~node20(s8))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9342, 9341])).
% 1.61/1.58 tff(9344,plain,
% 1.61/1.58 (~node20(s8)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9343, 8579, 9340])).
% 1.61/1.58 tff(9345,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state1(s7, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state1(s7, c_t1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9346,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s7, c_n1)) | (~m_main_v_state1(s7, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9347,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s7, c_n1)) | (~m_main_v_state1(s7, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9346, 9345])).
% 1.61/1.58 tff(9348,plain,
% 1.61/1.58 (~m_main_v_state1(s7, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9347, 17, 974])).
% 1.61/1.58 tff(9349,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s7, c_t1) | (~node20(s7)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s7, c_t1) | (~node20(s7)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9350,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s7, c_t1) | (~node20(s7)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9351,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s7, c_t1) | (~node20(s7))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9350, 9349])).
% 1.61/1.58 tff(9352,plain,
% 1.61/1.58 (~node20(s7)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9351, 8546, 9348])).
% 1.61/1.58 tff(9353,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s6)) | (~m_main_v_state1(s6, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s6)) | (~m_main_v_state1(s6, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9354,plain,
% 1.61/1.58 (((~m_main_v_state1(s6, c_c1)) | (~always19(s6))) <=> ((~always19(s6)) | (~m_main_v_state1(s6, c_c1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9355,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s6, c_c1)) | (~always19(s6)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s6)) | (~m_main_v_state1(s6, c_c1))))),
% 1.61/1.58 inference(monotonicity,[status(thm)],[9354])).
% 1.61/1.58 tff(9356,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s6, c_c1)) | (~always19(s6)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s6)) | (~m_main_v_state1(s6, c_c1)))),
% 1.61/1.58 inference(transitivity,[status(thm)],[9355, 9353])).
% 1.61/1.58 tff(9357,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s6, c_c1)) | (~always19(s6)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9358,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s6)) | (~m_main_v_state1(s6, c_c1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9357, 9356])).
% 1.61/1.58 tff(9359,plain,
% 1.61/1.58 (~always19(s6)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9358, 3439, 900])).
% 1.61/1.58 tff(9360,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s5, s6)) | (~always19(s5)) | always19(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s5, s6)) | (~always19(s5)) | always19(s6))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9361,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s5, s6)) | (~always19(s5)) | always19(s6))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9362,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s5, s6)) | (~always19(s5)) | always19(s6)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9361, 9360])).
% 1.61/1.58 tff(9363,plain,
% 1.61/1.58 ((~always19(s5)) | always19(s6)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9362, 8567, 878])).
% 1.61/1.58 tff(9364,plain,
% 1.61/1.58 (~always19(s5)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9363, 9359])).
% 1.61/1.58 tff(9365,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s5) | (~node20(s5)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s5) | (~node20(s5)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9366,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s5) | (~node20(s5)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9367,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s5) | (~node20(s5))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9366, 9365])).
% 1.61/1.58 tff(9368,plain,
% 1.61/1.58 (~node20(s5)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9367, 8579, 9364])).
% 1.61/1.58 tff(9369,plain,
% 1.61/1.58 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s4, s5)) | (~always19(s4)) | always19(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s4, s5)) | (~always19(s4)) | always19(s5))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9370,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s4, s5)) | (~always19(s4)) | always19(s5))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9371,plain,
% 1.61/1.58 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s4, s5)) | (~always19(s4)) | always19(s5)),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9370, 9369])).
% 1.61/1.58 tff(9372,plain,
% 1.61/1.58 ((~always19(s4)) | always19(s5)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9371, 8567, 712])).
% 1.61/1.58 tff(9373,plain,
% 1.61/1.58 (~always19(s4)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9372, 9364])).
% 1.61/1.58 tff(9374,plain,
% 1.61/1.58 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s4) | (~node20(s4)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s4) | (~node20(s4)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9375,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s4) | (~node20(s4)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9376,plain,
% 1.61/1.58 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s4) | (~node20(s4))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9375, 9374])).
% 1.61/1.58 tff(9377,plain,
% 1.61/1.58 (~node20(s4)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9376, 8579, 9373])).
% 1.61/1.58 tff(9378,plain,
% 1.61/1.58 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state1(s3, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state1(s3, c_t1)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9379,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s3, c_n1)) | (~m_main_v_state1(s3, c_t1)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9380,plain,
% 1.61/1.58 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s3, c_n1)) | (~m_main_v_state1(s3, c_t1))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9379, 9378])).
% 1.61/1.58 tff(9381,plain,
% 1.61/1.58 (~m_main_v_state1(s3, c_t1)),
% 1.61/1.58 inference(unit_resolution,[status(thm)],[9380, 17, 592])).
% 1.61/1.58 tff(9382,plain,
% 1.61/1.58 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s3, c_t1) | (~node20(s3)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s3, c_t1) | (~node20(s3)))),
% 1.61/1.58 inference(rewrite,[status(thm)],[])).
% 1.61/1.58 tff(9383,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s3, c_t1) | (~node20(s3)))),
% 1.61/1.58 inference(quant_inst,[status(thm)],[])).
% 1.61/1.58 tff(9384,plain,
% 1.61/1.58 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s3, c_t1) | (~node20(s3))),
% 1.61/1.58 inference(modus_ponens,[status(thm)],[9383, 9382])).
% 1.61/1.59 tff(9385,plain,
% 1.61/1.59 (~node20(s3)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9384, 8546, 9381])).
% 1.61/1.59 tff(9386,plain,
% 1.61/1.59 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s2)) | (~m_main_v_state1(s2, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s2)) | (~m_main_v_state1(s2, c_c1)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9387,plain,
% 1.61/1.59 (((~m_main_v_state1(s2, c_c1)) | (~always19(s2))) <=> ((~always19(s2)) | (~m_main_v_state1(s2, c_c1)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9388,plain,
% 1.61/1.59 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s2, c_c1)) | (~always19(s2)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~always19(s2)) | (~m_main_v_state1(s2, c_c1))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9387])).
% 1.61/1.59 tff(9389,plain,
% 1.61/1.59 (((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s2, c_c1)) | (~always19(s2)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s2)) | (~m_main_v_state1(s2, c_c1)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9388, 9386])).
% 1.61/1.59 tff(9390,plain,
% 1.61/1.59 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | ((~m_main_v_state1(s2, c_c1)) | (~always19(s2)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9391,plain,
% 1.61/1.59 ((~![X: $i] : ((~m_main_v_state1(X, c_c1)) | (~always19(X)))) | (~always19(s2)) | (~m_main_v_state1(s2, c_c1))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9390, 9389])).
% 1.61/1.59 tff(9392,plain,
% 1.61/1.59 (~always19(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9391, 3439, 447])).
% 1.61/1.59 tff(9393,plain,
% 1.61/1.59 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s2) | (~node20(s2)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s2) | (~node20(s2)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9394,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s2) | (~node20(s2)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9395,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s2) | (~node20(s2))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9394, 9393])).
% 1.61/1.59 tff(9396,plain,
% 1.61/1.59 (~node20(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9395, 8579, 9392])).
% 1.61/1.59 tff(9397,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s1, s2)) | (~always19(s1)) | always19(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s1, s2)) | (~always19(s1)) | always19(s2))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9398,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s1, s2)) | (~always19(s1)) | always19(s2))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9399,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s1, s2)) | (~always19(s1)) | always19(s2)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9398, 9397])).
% 1.61/1.59 tff(9400,plain,
% 1.61/1.59 ((~always19(s1)) | always19(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9399, 8567, 282])).
% 1.61/1.59 tff(9401,plain,
% 1.61/1.59 (~always19(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9400, 9392])).
% 1.61/1.59 tff(9402,plain,
% 1.61/1.59 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s1) | (~node20(s1)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s1) | (~node20(s1)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9403,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s1) | (~node20(s1)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9404,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s1) | (~node20(s1))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9403, 9402])).
% 1.61/1.59 tff(9405,plain,
% 1.61/1.59 (~node20(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9404, 8579, 9401])).
% 1.61/1.59 tff(9406,plain,
% 1.61/1.59 (((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s0, c_t1) | (~node20(s0)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s0, c_t1) | (~node20(s0)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9407,plain,
% 1.61/1.59 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | (m_main_v_state1(s0, c_t1) | (~node20(s0)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9408,plain,
% 1.61/1.59 ((~![X: $i] : (m_main_v_state1(X, c_t1) | (~node20(X)))) | m_main_v_state1(s0, c_t1) | (~node20(s0))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9407, 9406])).
% 1.61/1.59 tff(9409,plain,
% 1.61/1.59 (~node20(s0)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9408, 8546, 21])).
% 1.61/1.59 tff(9410,plain,
% 1.61/1.59 (until21(s0) <=> until21(s0)),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9411,axiom,(until21(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty13')).
% 1.61/1.59 tff(9412,plain,
% 1.61/1.59 (until21(s0)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9411, 9410])).
% 1.61/1.59 tff(9413,plain,
% 1.61/1.59 (^[X: $i] : refl((node20(X) | (~until21(X)) | xuntil22(X)) <=> (node20(X) | (~until21(X)) | xuntil22(X)))),
% 1.61/1.59 inference(bind,[status(th)],[])).
% 1.61/1.59 tff(9414,plain,
% 1.61/1.59 (![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X)) <=> ![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(quant_intro,[status(thm)],[9413])).
% 1.61/1.59 tff(9415,plain,
% 1.61/1.59 (![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X)) <=> ![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9416,plain,
% 1.61/1.59 (^[X: $i] : rewrite(((node20(X) | xuntil22(X)) | (~until21(X))) <=> (node20(X) | (~until21(X)) | xuntil22(X)))),
% 1.61/1.59 inference(bind,[status(th)],[])).
% 1.61/1.59 tff(9417,plain,
% 1.61/1.59 (![X: $i] : ((node20(X) | xuntil22(X)) | (~until21(X))) <=> ![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(quant_intro,[status(thm)],[9416])).
% 1.61/1.59 tff(9418,axiom,(![X: $i] : ((node20(X) | xuntil22(X)) | (~until21(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 1.61/1.59 tff(9419,plain,
% 1.61/1.59 (![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9418, 9417])).
% 1.61/1.59 tff(9420,plain,
% 1.61/1.59 (![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9419, 9415])).
% 1.61/1.59 tff(9421,plain,(
% 1.61/1.59 ![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(skolemize,[status(sab)],[9420])).
% 1.61/1.59 tff(9422,plain,
% 1.61/1.59 (![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9421, 9414])).
% 1.61/1.59 tff(9423,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s0) | node20(s0) | (~until21(s0)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s0) | node20(s0) | (~until21(s0)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9424,plain,
% 1.61/1.59 ((node20(s0) | (~until21(s0)) | xuntil22(s0)) <=> (xuntil22(s0) | node20(s0) | (~until21(s0)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9425,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s0) | (~until21(s0)) | xuntil22(s0))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s0) | node20(s0) | (~until21(s0))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9424])).
% 1.61/1.59 tff(9426,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s0) | (~until21(s0)) | xuntil22(s0))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s0) | node20(s0) | (~until21(s0)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9425, 9423])).
% 1.61/1.59 tff(9427,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s0) | (~until21(s0)) | xuntil22(s0))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9428,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s0) | node20(s0) | (~until21(s0))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9427, 9426])).
% 1.61/1.59 tff(9429,plain,
% 1.61/1.59 (xuntil22(s0) | node20(s0)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9428, 9422, 9412])).
% 1.61/1.59 tff(9430,plain,
% 1.61/1.59 (xuntil22(s0)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9429, 9409])).
% 1.61/1.59 tff(9431,plain,
% 1.61/1.59 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil22(X)) | until21(Y)) <=> ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y)))),
% 1.61/1.59 inference(bind,[status(th)],[])).
% 1.61/1.59 tff(9432,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(quant_intro,[status(thm)],[9431])).
% 1.61/1.59 tff(9433,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9434,plain,
% 1.61/1.59 (^[Y: $i, X: $i] : rewrite(((until21(Y) | (~succ(X, Y))) | (~xuntil22(X))) <=> ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y)))),
% 1.61/1.59 inference(bind,[status(th)],[])).
% 1.61/1.59 tff(9435,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((until21(Y) | (~succ(X, Y))) | (~xuntil22(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(quant_intro,[status(thm)],[9434])).
% 1.61/1.59 tff(9436,axiom,(![Y: $i, X: $i] : ((until21(Y) | (~succ(X, Y))) | (~xuntil22(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 1.61/1.59 tff(9437,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9436, 9435])).
% 1.61/1.59 tff(9438,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9437, 9433])).
% 1.61/1.59 tff(9439,plain,(
% 1.61/1.59 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(skolemize,[status(sab)],[9438])).
% 1.61/1.59 tff(9440,plain,
% 1.61/1.59 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9439, 9432])).
% 1.61/1.59 tff(9441,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s0, s1)) | (~xuntil22(s0)) | until21(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s0, s1)) | (~xuntil22(s0)) | until21(s1))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9442,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s0, s1)) | (~xuntil22(s0)) | until21(s1))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9443,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s0, s1)) | (~xuntil22(s0)) | until21(s1)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9442, 9441])).
% 1.61/1.59 tff(9444,plain,
% 1.61/1.59 ((~xuntil22(s0)) | until21(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9443, 42, 9440])).
% 1.61/1.59 tff(9445,plain,
% 1.61/1.59 (until21(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9444, 9430])).
% 1.61/1.59 tff(9446,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s1) | node20(s1) | (~until21(s1)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s1) | node20(s1) | (~until21(s1)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9447,plain,
% 1.61/1.59 ((node20(s1) | (~until21(s1)) | xuntil22(s1)) <=> (xuntil22(s1) | node20(s1) | (~until21(s1)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9448,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s1) | (~until21(s1)) | xuntil22(s1))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s1) | node20(s1) | (~until21(s1))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9447])).
% 1.61/1.59 tff(9449,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s1) | (~until21(s1)) | xuntil22(s1))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s1) | node20(s1) | (~until21(s1)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9448, 9446])).
% 1.61/1.59 tff(9450,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s1) | (~until21(s1)) | xuntil22(s1))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9451,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s1) | node20(s1) | (~until21(s1))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9450, 9449])).
% 1.61/1.59 tff(9452,plain,
% 1.61/1.59 (xuntil22(s1) | node20(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9451, 9422, 9445])).
% 1.61/1.59 tff(9453,plain,
% 1.61/1.59 (xuntil22(s1)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9452, 9405])).
% 1.61/1.59 tff(9454,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s1, s2)) | (~xuntil22(s1)) | until21(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s1, s2)) | (~xuntil22(s1)) | until21(s2))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9455,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s1, s2)) | (~xuntil22(s1)) | until21(s2))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9456,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s1, s2)) | (~xuntil22(s1)) | until21(s2)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9455, 9454])).
% 1.61/1.59 tff(9457,plain,
% 1.61/1.59 ((~xuntil22(s1)) | until21(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9456, 278, 9440])).
% 1.61/1.59 tff(9458,plain,
% 1.61/1.59 (until21(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9457, 9453])).
% 1.61/1.59 tff(9459,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s2) | node20(s2) | (~until21(s2)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s2) | node20(s2) | (~until21(s2)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9460,plain,
% 1.61/1.59 ((node20(s2) | (~until21(s2)) | xuntil22(s2)) <=> (xuntil22(s2) | node20(s2) | (~until21(s2)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9461,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s2) | (~until21(s2)) | xuntil22(s2))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s2) | node20(s2) | (~until21(s2))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9460])).
% 1.61/1.59 tff(9462,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s2) | (~until21(s2)) | xuntil22(s2))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s2) | node20(s2) | (~until21(s2)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9461, 9459])).
% 1.61/1.59 tff(9463,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s2) | (~until21(s2)) | xuntil22(s2))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9464,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s2) | node20(s2) | (~until21(s2))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9463, 9462])).
% 1.61/1.59 tff(9465,plain,
% 1.61/1.59 (xuntil22(s2)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9464, 9422, 9458, 9396])).
% 1.61/1.59 tff(9466,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s2, s3)) | (~xuntil22(s2)) | until21(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s2, s3)) | (~xuntil22(s2)) | until21(s3))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9467,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s2, s3)) | (~xuntil22(s2)) | until21(s3))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9468,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s2, s3)) | (~xuntil22(s2)) | until21(s3)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9467, 9466])).
% 1.61/1.59 tff(9469,plain,
% 1.61/1.59 ((~xuntil22(s2)) | until21(s3)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9468, 480, 9440])).
% 1.61/1.59 tff(9470,plain,
% 1.61/1.59 (until21(s3)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9469, 9465])).
% 1.61/1.59 tff(9471,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s3) | node20(s3) | (~until21(s3)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s3) | node20(s3) | (~until21(s3)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9472,plain,
% 1.61/1.59 ((node20(s3) | (~until21(s3)) | xuntil22(s3)) <=> (xuntil22(s3) | node20(s3) | (~until21(s3)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9473,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s3) | (~until21(s3)) | xuntil22(s3))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s3) | node20(s3) | (~until21(s3))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9472])).
% 1.61/1.59 tff(9474,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s3) | (~until21(s3)) | xuntil22(s3))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s3) | node20(s3) | (~until21(s3)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9473, 9471])).
% 1.61/1.59 tff(9475,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s3) | (~until21(s3)) | xuntil22(s3))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9476,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s3) | node20(s3) | (~until21(s3))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9475, 9474])).
% 1.61/1.59 tff(9477,plain,
% 1.61/1.59 (xuntil22(s3)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9476, 9422, 9470, 9385])).
% 1.61/1.59 tff(9478,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s3, s4)) | (~xuntil22(s3)) | until21(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s3, s4)) | (~xuntil22(s3)) | until21(s4))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9479,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s3, s4)) | (~xuntil22(s3)) | until21(s4))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9480,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s3, s4)) | (~xuntil22(s3)) | until21(s4)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9479, 9478])).
% 1.61/1.59 tff(9481,plain,
% 1.61/1.59 ((~xuntil22(s3)) | until21(s4)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9480, 599, 9440])).
% 1.61/1.59 tff(9482,plain,
% 1.61/1.59 (until21(s4)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9481, 9477])).
% 1.61/1.59 tff(9483,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s4) | node20(s4) | (~until21(s4)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s4) | node20(s4) | (~until21(s4)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9484,plain,
% 1.61/1.59 ((node20(s4) | (~until21(s4)) | xuntil22(s4)) <=> (xuntil22(s4) | node20(s4) | (~until21(s4)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9485,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s4) | (~until21(s4)) | xuntil22(s4))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s4) | node20(s4) | (~until21(s4))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9484])).
% 1.61/1.59 tff(9486,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s4) | (~until21(s4)) | xuntil22(s4))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s4) | node20(s4) | (~until21(s4)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9485, 9483])).
% 1.61/1.59 tff(9487,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s4) | (~until21(s4)) | xuntil22(s4))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9488,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s4) | node20(s4) | (~until21(s4))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9487, 9486])).
% 1.61/1.59 tff(9489,plain,
% 1.61/1.59 (xuntil22(s4) | node20(s4)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9488, 9422, 9482])).
% 1.61/1.59 tff(9490,plain,
% 1.61/1.59 (xuntil22(s4)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9489, 9377])).
% 1.61/1.59 tff(9491,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s4, s5)) | (~xuntil22(s4)) | until21(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s4, s5)) | (~xuntil22(s4)) | until21(s5))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9492,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s4, s5)) | (~xuntil22(s4)) | until21(s5))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9493,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s4, s5)) | (~xuntil22(s4)) | until21(s5)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9492, 9491])).
% 1.61/1.59 tff(9494,plain,
% 1.61/1.59 ((~xuntil22(s4)) | until21(s5)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9493, 708, 9440])).
% 1.61/1.59 tff(9495,plain,
% 1.61/1.59 (until21(s5)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9494, 9490])).
% 1.61/1.59 tff(9496,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s5) | node20(s5) | (~until21(s5)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s5) | node20(s5) | (~until21(s5)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9497,plain,
% 1.61/1.59 ((node20(s5) | (~until21(s5)) | xuntil22(s5)) <=> (xuntil22(s5) | node20(s5) | (~until21(s5)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9498,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s5) | (~until21(s5)) | xuntil22(s5))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s5) | node20(s5) | (~until21(s5))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9497])).
% 1.61/1.59 tff(9499,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s5) | (~until21(s5)) | xuntil22(s5))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s5) | node20(s5) | (~until21(s5)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9498, 9496])).
% 1.61/1.59 tff(9500,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s5) | (~until21(s5)) | xuntil22(s5))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9501,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s5) | node20(s5) | (~until21(s5))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9500, 9499])).
% 1.61/1.59 tff(9502,plain,
% 1.61/1.59 (xuntil22(s5)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9501, 9422, 9495, 9368])).
% 1.61/1.59 tff(9503,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s5, s6)) | (~xuntil22(s5)) | until21(s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s5, s6)) | (~xuntil22(s5)) | until21(s6))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9504,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s5, s6)) | (~xuntil22(s5)) | until21(s6))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9505,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s5, s6)) | (~xuntil22(s5)) | until21(s6)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9504, 9503])).
% 1.61/1.59 tff(9506,plain,
% 1.61/1.59 ((~xuntil22(s5)) | until21(s6)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9505, 874, 9440])).
% 1.61/1.59 tff(9507,plain,
% 1.61/1.59 (until21(s6)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9506, 9502])).
% 1.61/1.59 tff(9508,plain,
% 1.61/1.59 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s6) | (~node20(s6)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s6) | (~node20(s6)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9509,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s6) | (~node20(s6)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9510,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s6) | (~node20(s6))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9509, 9508])).
% 1.61/1.59 tff(9511,plain,
% 1.61/1.59 (~node20(s6)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9510, 8579, 9359])).
% 1.61/1.59 tff(9512,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s6) | node20(s6) | (~until21(s6)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s6) | node20(s6) | (~until21(s6)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9513,plain,
% 1.61/1.59 ((node20(s6) | (~until21(s6)) | xuntil22(s6)) <=> (xuntil22(s6) | node20(s6) | (~until21(s6)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9514,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s6) | (~until21(s6)) | xuntil22(s6))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s6) | node20(s6) | (~until21(s6))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9513])).
% 1.61/1.59 tff(9515,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s6) | (~until21(s6)) | xuntil22(s6))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s6) | node20(s6) | (~until21(s6)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9514, 9512])).
% 1.61/1.59 tff(9516,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s6) | (~until21(s6)) | xuntil22(s6))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9517,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s6) | node20(s6) | (~until21(s6))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9516, 9515])).
% 1.61/1.59 tff(9518,plain,
% 1.61/1.59 (xuntil22(s6) | (~until21(s6))),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9517, 9422, 9511])).
% 1.61/1.59 tff(9519,plain,
% 1.61/1.59 (xuntil22(s6)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9518, 9507])).
% 1.61/1.59 tff(9520,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s6, s7)) | (~xuntil22(s6)) | until21(s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s6, s7)) | (~xuntil22(s6)) | until21(s7))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9521,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s6, s7)) | (~xuntil22(s6)) | until21(s7))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9522,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s6, s7)) | (~xuntil22(s6)) | until21(s7)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9521, 9520])).
% 1.61/1.59 tff(9523,plain,
% 1.61/1.59 ((~xuntil22(s6)) | until21(s7)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9522, 958, 9440])).
% 1.61/1.59 tff(9524,plain,
% 1.61/1.59 (until21(s7)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9523, 9519])).
% 1.61/1.59 tff(9525,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s7) | node20(s7) | (~until21(s7)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s7) | node20(s7) | (~until21(s7)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9526,plain,
% 1.61/1.59 ((node20(s7) | (~until21(s7)) | xuntil22(s7)) <=> (xuntil22(s7) | node20(s7) | (~until21(s7)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9527,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s7) | (~until21(s7)) | xuntil22(s7))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s7) | node20(s7) | (~until21(s7))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9526])).
% 1.61/1.59 tff(9528,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s7) | (~until21(s7)) | xuntil22(s7))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s7) | node20(s7) | (~until21(s7)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9527, 9525])).
% 1.61/1.59 tff(9529,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s7) | (~until21(s7)) | xuntil22(s7))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9530,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s7) | node20(s7) | (~until21(s7))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9529, 9528])).
% 1.61/1.59 tff(9531,plain,
% 1.61/1.59 (xuntil22(s7)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9530, 9422, 9524, 9352])).
% 1.61/1.59 tff(9532,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s7, s8)) | (~xuntil22(s7)) | until21(s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s7, s8)) | (~xuntil22(s7)) | until21(s8))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9533,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s7, s8)) | (~xuntil22(s7)) | until21(s8))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9534,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s7, s8)) | (~xuntil22(s7)) | until21(s8)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9533, 9532])).
% 1.61/1.59 tff(9535,plain,
% 1.61/1.59 ((~xuntil22(s7)) | until21(s8)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9534, 1043, 9440])).
% 1.61/1.59 tff(9536,plain,
% 1.61/1.59 (until21(s8)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9535, 9531])).
% 1.61/1.59 tff(9537,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s8) | node20(s8) | (~until21(s8)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s8) | node20(s8) | (~until21(s8)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9538,plain,
% 1.61/1.59 ((node20(s8) | (~until21(s8)) | xuntil22(s8)) <=> (xuntil22(s8) | node20(s8) | (~until21(s8)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9539,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s8) | (~until21(s8)) | xuntil22(s8))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s8) | node20(s8) | (~until21(s8))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9538])).
% 1.61/1.59 tff(9540,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s8) | (~until21(s8)) | xuntil22(s8))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s8) | node20(s8) | (~until21(s8)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9539, 9537])).
% 1.61/1.59 tff(9541,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s8) | (~until21(s8)) | xuntil22(s8))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9542,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s8) | node20(s8) | (~until21(s8))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9541, 9540])).
% 1.61/1.59 tff(9543,plain,
% 1.61/1.59 (xuntil22(s8) | node20(s8)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9542, 9422, 9536])).
% 1.61/1.59 tff(9544,plain,
% 1.61/1.59 (xuntil22(s8)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9543, 9344])).
% 1.61/1.59 tff(9545,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s8, s9)) | (~xuntil22(s8)) | until21(s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s8, s9)) | (~xuntil22(s8)) | until21(s9))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9546,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s8, s9)) | (~xuntil22(s8)) | until21(s9))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9547,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s8, s9)) | (~xuntil22(s8)) | until21(s9)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9546, 9545])).
% 1.61/1.59 tff(9548,plain,
% 1.61/1.59 ((~xuntil22(s8)) | until21(s9)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9547, 1132, 9440])).
% 1.61/1.59 tff(9549,plain,
% 1.61/1.59 (until21(s9)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9548, 9544])).
% 1.61/1.59 tff(9550,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s9) | node20(s9) | (~until21(s9)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s9) | node20(s9) | (~until21(s9)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9551,plain,
% 1.61/1.59 ((node20(s9) | (~until21(s9)) | xuntil22(s9)) <=> (xuntil22(s9) | node20(s9) | (~until21(s9)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9552,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s9) | (~until21(s9)) | xuntil22(s9))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s9) | node20(s9) | (~until21(s9))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9551])).
% 1.61/1.59 tff(9553,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s9) | (~until21(s9)) | xuntil22(s9))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s9) | node20(s9) | (~until21(s9)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9552, 9550])).
% 1.61/1.59 tff(9554,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s9) | (~until21(s9)) | xuntil22(s9))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9555,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s9) | node20(s9) | (~until21(s9))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9554, 9553])).
% 1.61/1.59 tff(9556,plain,
% 1.61/1.59 (xuntil22(s9)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9555, 9422, 9549, 9335])).
% 1.61/1.59 tff(9557,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s9, s10)) | (~xuntil22(s9)) | until21(s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s9, s10)) | (~xuntil22(s9)) | until21(s10))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9558,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s9, s10)) | (~xuntil22(s9)) | until21(s10))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9559,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s9, s10)) | (~xuntil22(s9)) | until21(s10)),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9558, 9557])).
% 1.61/1.59 tff(9560,plain,
% 1.61/1.59 ((~xuntil22(s9)) | until21(s10)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9559, 1199, 9440])).
% 1.61/1.59 tff(9561,plain,
% 1.61/1.59 (until21(s10)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9560, 9556])).
% 1.61/1.59 tff(9562,plain,
% 1.61/1.59 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s10) | (~node20(s10)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s10) | (~node20(s10)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9563,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s10) | (~node20(s10)))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9564,plain,
% 1.61/1.59 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s10) | (~node20(s10))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9563, 9562])).
% 1.61/1.59 tff(9565,plain,
% 1.61/1.59 (~node20(s10)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9564, 8579, 9326])).
% 1.61/1.59 tff(9566,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s10) | node20(s10) | (~until21(s10)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s10) | node20(s10) | (~until21(s10)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9567,plain,
% 1.61/1.59 ((node20(s10) | (~until21(s10)) | xuntil22(s10)) <=> (xuntil22(s10) | node20(s10) | (~until21(s10)))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9568,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s10) | (~until21(s10)) | xuntil22(s10))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s10) | node20(s10) | (~until21(s10))))),
% 1.61/1.59 inference(monotonicity,[status(thm)],[9567])).
% 1.61/1.59 tff(9569,plain,
% 1.61/1.59 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s10) | (~until21(s10)) | xuntil22(s10))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s10) | node20(s10) | (~until21(s10)))),
% 1.61/1.59 inference(transitivity,[status(thm)],[9568, 9566])).
% 1.61/1.59 tff(9570,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s10) | (~until21(s10)) | xuntil22(s10))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9571,plain,
% 1.61/1.59 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s10) | node20(s10) | (~until21(s10))),
% 1.61/1.59 inference(modus_ponens,[status(thm)],[9570, 9569])).
% 1.61/1.59 tff(9572,plain,
% 1.61/1.59 (xuntil22(s10) | (~until21(s10))),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9571, 9422, 9565])).
% 1.61/1.59 tff(9573,plain,
% 1.61/1.59 (xuntil22(s10)),
% 1.61/1.59 inference(unit_resolution,[status(thm)],[9572, 9561])).
% 1.61/1.59 tff(9574,plain,
% 1.61/1.59 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s10, s11)) | (~xuntil22(s10)) | until21(s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s10, s11)) | (~xuntil22(s10)) | until21(s11))),
% 1.61/1.59 inference(rewrite,[status(thm)],[])).
% 1.61/1.59 tff(9575,plain,
% 1.61/1.59 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s10, s11)) | (~xuntil22(s10)) | until21(s11))),
% 1.61/1.59 inference(quant_inst,[status(thm)],[])).
% 1.61/1.59 tff(9576,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s10, s11)) | (~xuntil22(s10)) | until21(s11)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9575, 9574])).
% 1.61/1.60 tff(9577,plain,
% 1.61/1.60 ((~xuntil22(s10)) | until21(s11)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9576, 1298, 9440])).
% 1.61/1.60 tff(9578,plain,
% 1.61/1.60 (until21(s11)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9577, 9573])).
% 1.61/1.60 tff(9579,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s11) | node20(s11) | (~until21(s11)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s11) | node20(s11) | (~until21(s11)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9580,plain,
% 1.61/1.60 ((node20(s11) | (~until21(s11)) | xuntil22(s11)) <=> (xuntil22(s11) | node20(s11) | (~until21(s11)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9581,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s11) | (~until21(s11)) | xuntil22(s11))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s11) | node20(s11) | (~until21(s11))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9580])).
% 1.61/1.60 tff(9582,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s11) | (~until21(s11)) | xuntil22(s11))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s11) | node20(s11) | (~until21(s11)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9581, 9579])).
% 1.61/1.60 tff(9583,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s11) | (~until21(s11)) | xuntil22(s11))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9584,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s11) | node20(s11) | (~until21(s11))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9583, 9582])).
% 1.61/1.60 tff(9585,plain,
% 1.61/1.60 (xuntil22(s11)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9584, 9422, 9578, 9319])).
% 1.61/1.60 tff(9586,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s11, s12)) | (~xuntil22(s11)) | until21(s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s11, s12)) | (~xuntil22(s11)) | until21(s12))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9587,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s11, s12)) | (~xuntil22(s11)) | until21(s12))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9588,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s11, s12)) | (~xuntil22(s11)) | until21(s12)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9587, 9586])).
% 1.61/1.60 tff(9589,plain,
% 1.61/1.60 ((~xuntil22(s11)) | until21(s12)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9588, 1376, 9440])).
% 1.61/1.60 tff(9590,plain,
% 1.61/1.60 (until21(s12)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9589, 9585])).
% 1.61/1.60 tff(9591,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s12) | node20(s12) | (~until21(s12)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s12) | node20(s12) | (~until21(s12)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9592,plain,
% 1.61/1.60 ((node20(s12) | (~until21(s12)) | xuntil22(s12)) <=> (xuntil22(s12) | node20(s12) | (~until21(s12)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9593,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s12) | (~until21(s12)) | xuntil22(s12))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s12) | node20(s12) | (~until21(s12))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9592])).
% 1.61/1.60 tff(9594,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s12) | (~until21(s12)) | xuntil22(s12))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s12) | node20(s12) | (~until21(s12)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9593, 9591])).
% 1.61/1.60 tff(9595,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s12) | (~until21(s12)) | xuntil22(s12))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9596,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s12) | node20(s12) | (~until21(s12))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9595, 9594])).
% 1.61/1.60 tff(9597,plain,
% 1.61/1.60 (xuntil22(s12) | node20(s12)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9596, 9422, 9590])).
% 1.61/1.60 tff(9598,plain,
% 1.61/1.60 (xuntil22(s12)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9597, 9311])).
% 1.61/1.60 tff(9599,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s12, s13)) | (~xuntil22(s12)) | until21(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s12, s13)) | (~xuntil22(s12)) | until21(s13))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9600,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s12, s13)) | (~xuntil22(s12)) | until21(s13))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9601,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s12, s13)) | (~xuntil22(s12)) | until21(s13)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9600, 9599])).
% 1.61/1.60 tff(9602,plain,
% 1.61/1.60 ((~xuntil22(s12)) | until21(s13)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9601, 1437, 9440])).
% 1.61/1.60 tff(9603,plain,
% 1.61/1.60 (until21(s13)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9602, 9598])).
% 1.61/1.60 tff(9604,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s13) | node20(s13) | (~until21(s13)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s13) | node20(s13) | (~until21(s13)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9605,plain,
% 1.61/1.60 ((node20(s13) | (~until21(s13)) | xuntil22(s13)) <=> (xuntil22(s13) | node20(s13) | (~until21(s13)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9606,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s13) | (~until21(s13)) | xuntil22(s13))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s13) | node20(s13) | (~until21(s13))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9605])).
% 1.61/1.60 tff(9607,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s13) | (~until21(s13)) | xuntil22(s13))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s13) | node20(s13) | (~until21(s13)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9606, 9604])).
% 1.61/1.60 tff(9608,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s13) | (~until21(s13)) | xuntil22(s13))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9609,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s13) | node20(s13) | (~until21(s13))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9608, 9607])).
% 1.61/1.60 tff(9610,plain,
% 1.61/1.60 (xuntil22(s13)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9609, 9422, 9603, 9302])).
% 1.61/1.60 tff(9611,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s13, s14)) | (~xuntil22(s13)) | until21(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s13, s14)) | (~xuntil22(s13)) | until21(s14))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9612,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s13, s14)) | (~xuntil22(s13)) | until21(s14))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9613,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s13, s14)) | (~xuntil22(s13)) | until21(s14)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9612, 9611])).
% 1.61/1.60 tff(9614,plain,
% 1.61/1.60 ((~xuntil22(s13)) | until21(s14)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9613, 1532, 9440])).
% 1.61/1.60 tff(9615,plain,
% 1.61/1.60 (until21(s14)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9614, 9610])).
% 1.61/1.60 tff(9616,plain,
% 1.61/1.60 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s14) | (~node20(s14)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s14) | (~node20(s14)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9617,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s14) | (~node20(s14)))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9618,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s14) | (~node20(s14))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9617, 9616])).
% 1.61/1.60 tff(9619,plain,
% 1.61/1.60 (~node20(s14)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9618, 8579, 9293])).
% 1.61/1.60 tff(9620,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s14) | node20(s14) | (~until21(s14)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s14) | node20(s14) | (~until21(s14)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9621,plain,
% 1.61/1.60 ((node20(s14) | (~until21(s14)) | xuntil22(s14)) <=> (xuntil22(s14) | node20(s14) | (~until21(s14)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9622,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s14) | (~until21(s14)) | xuntil22(s14))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s14) | node20(s14) | (~until21(s14))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9621])).
% 1.61/1.60 tff(9623,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s14) | (~until21(s14)) | xuntil22(s14))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s14) | node20(s14) | (~until21(s14)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9622, 9620])).
% 1.61/1.60 tff(9624,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s14) | (~until21(s14)) | xuntil22(s14))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9625,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s14) | node20(s14) | (~until21(s14))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9624, 9623])).
% 1.61/1.60 tff(9626,plain,
% 1.61/1.60 (xuntil22(s14) | (~until21(s14))),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9625, 9422, 9619])).
% 1.61/1.60 tff(9627,plain,
% 1.61/1.60 (xuntil22(s14)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9626, 9615])).
% 1.61/1.60 tff(9628,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s14, s15)) | (~xuntil22(s14)) | until21(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s14, s15)) | (~xuntil22(s14)) | until21(s15))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9629,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s14, s15)) | (~xuntil22(s14)) | until21(s15))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9630,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s14, s15)) | (~xuntil22(s14)) | until21(s15)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9629, 9628])).
% 1.61/1.60 tff(9631,plain,
% 1.61/1.60 ((~xuntil22(s14)) | until21(s15)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9630, 1596, 9440])).
% 1.61/1.60 tff(9632,plain,
% 1.61/1.60 (until21(s15)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9631, 9627])).
% 1.61/1.60 tff(9633,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s15) | node20(s15) | (~until21(s15)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s15) | node20(s15) | (~until21(s15)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9634,plain,
% 1.61/1.60 ((node20(s15) | (~until21(s15)) | xuntil22(s15)) <=> (xuntil22(s15) | node20(s15) | (~until21(s15)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9635,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s15) | (~until21(s15)) | xuntil22(s15))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s15) | node20(s15) | (~until21(s15))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9634])).
% 1.61/1.60 tff(9636,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s15) | (~until21(s15)) | xuntil22(s15))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s15) | node20(s15) | (~until21(s15)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9635, 9633])).
% 1.61/1.60 tff(9637,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s15) | (~until21(s15)) | xuntil22(s15))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9638,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s15) | node20(s15) | (~until21(s15))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9637, 9636])).
% 1.61/1.60 tff(9639,plain,
% 1.61/1.60 (xuntil22(s15)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9638, 9422, 9632, 9286])).
% 1.61/1.60 tff(9640,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s15, s16)) | (~xuntil22(s15)) | until21(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s15, s16)) | (~xuntil22(s15)) | until21(s16))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9641,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s15, s16)) | (~xuntil22(s15)) | until21(s16))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9642,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s15, s16)) | (~xuntil22(s15)) | until21(s16)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9641, 9640])).
% 1.61/1.60 tff(9643,plain,
% 1.61/1.60 ((~xuntil22(s15)) | until21(s16)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9642, 1671, 9440])).
% 1.61/1.60 tff(9644,plain,
% 1.61/1.60 (until21(s16)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9643, 9639])).
% 1.61/1.60 tff(9645,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s16) | node20(s16) | (~until21(s16)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s16) | node20(s16) | (~until21(s16)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9646,plain,
% 1.61/1.60 ((node20(s16) | (~until21(s16)) | xuntil22(s16)) <=> (xuntil22(s16) | node20(s16) | (~until21(s16)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9647,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s16) | (~until21(s16)) | xuntil22(s16))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s16) | node20(s16) | (~until21(s16))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9646])).
% 1.61/1.60 tff(9648,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s16) | (~until21(s16)) | xuntil22(s16))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s16) | node20(s16) | (~until21(s16)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9647, 9645])).
% 1.61/1.60 tff(9649,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s16) | (~until21(s16)) | xuntil22(s16))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9650,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s16) | node20(s16) | (~until21(s16))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9649, 9648])).
% 1.61/1.60 tff(9651,plain,
% 1.61/1.60 (xuntil22(s16) | node20(s16)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9650, 9422, 9644])).
% 1.61/1.60 tff(9652,plain,
% 1.61/1.60 (xuntil22(s16)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9651, 9278])).
% 1.61/1.60 tff(9653,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s16, s17)) | (~xuntil22(s16)) | until21(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s16, s17)) | (~xuntil22(s16)) | until21(s17))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9654,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s16, s17)) | (~xuntil22(s16)) | until21(s17))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9655,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s16, s17)) | (~xuntil22(s16)) | until21(s17)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9654, 9653])).
% 1.61/1.60 tff(9656,plain,
% 1.61/1.60 ((~xuntil22(s16)) | until21(s17)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9655, 1760, 9440])).
% 1.61/1.60 tff(9657,plain,
% 1.61/1.60 (until21(s17)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9656, 9652])).
% 1.61/1.60 tff(9658,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s17) | node20(s17) | (~until21(s17)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s17) | node20(s17) | (~until21(s17)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9659,plain,
% 1.61/1.60 ((node20(s17) | (~until21(s17)) | xuntil22(s17)) <=> (xuntil22(s17) | node20(s17) | (~until21(s17)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9660,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s17) | (~until21(s17)) | xuntil22(s17))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s17) | node20(s17) | (~until21(s17))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9659])).
% 1.61/1.60 tff(9661,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s17) | (~until21(s17)) | xuntil22(s17))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s17) | node20(s17) | (~until21(s17)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9660, 9658])).
% 1.61/1.60 tff(9662,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s17) | (~until21(s17)) | xuntil22(s17))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9663,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s17) | node20(s17) | (~until21(s17))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9662, 9661])).
% 1.61/1.60 tff(9664,plain,
% 1.61/1.60 (xuntil22(s17)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9663, 9422, 9657, 9269])).
% 1.61/1.60 tff(9665,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s17, s18)) | (~xuntil22(s17)) | until21(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s17, s18)) | (~xuntil22(s17)) | until21(s18))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9666,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s17, s18)) | (~xuntil22(s17)) | until21(s18))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9667,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s17, s18)) | (~xuntil22(s17)) | until21(s18)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9666, 9665])).
% 1.61/1.60 tff(9668,plain,
% 1.61/1.60 ((~xuntil22(s17)) | until21(s18)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9667, 1827, 9440])).
% 1.61/1.60 tff(9669,plain,
% 1.61/1.60 (until21(s18)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9668, 9664])).
% 1.61/1.60 tff(9670,plain,
% 1.61/1.60 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s18) | (~node20(s18)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s18) | (~node20(s18)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9671,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s18) | (~node20(s18)))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9672,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s18) | (~node20(s18))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9671, 9670])).
% 1.61/1.60 tff(9673,plain,
% 1.61/1.60 (~node20(s18)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9672, 8579, 9260])).
% 1.61/1.60 tff(9674,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s18) | node20(s18) | (~until21(s18)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s18) | node20(s18) | (~until21(s18)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9675,plain,
% 1.61/1.60 ((node20(s18) | (~until21(s18)) | xuntil22(s18)) <=> (xuntil22(s18) | node20(s18) | (~until21(s18)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9676,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s18) | (~until21(s18)) | xuntil22(s18))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s18) | node20(s18) | (~until21(s18))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9675])).
% 1.61/1.60 tff(9677,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s18) | (~until21(s18)) | xuntil22(s18))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s18) | node20(s18) | (~until21(s18)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9676, 9674])).
% 1.61/1.60 tff(9678,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s18) | (~until21(s18)) | xuntil22(s18))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9679,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s18) | node20(s18) | (~until21(s18))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9678, 9677])).
% 1.61/1.60 tff(9680,plain,
% 1.61/1.60 (xuntil22(s18) | (~until21(s18))),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9679, 9422, 9673])).
% 1.61/1.60 tff(9681,plain,
% 1.61/1.60 (xuntil22(s18)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9680, 9669])).
% 1.61/1.60 tff(9682,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s18, s19)) | (~xuntil22(s18)) | until21(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s18, s19)) | (~xuntil22(s18)) | until21(s19))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9683,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s18, s19)) | (~xuntil22(s18)) | until21(s19))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9684,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s18, s19)) | (~xuntil22(s18)) | until21(s19)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9683, 9682])).
% 1.61/1.60 tff(9685,plain,
% 1.61/1.60 ((~xuntil22(s18)) | until21(s19)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9684, 1926, 9440])).
% 1.61/1.60 tff(9686,plain,
% 1.61/1.60 (until21(s19)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9685, 9681])).
% 1.61/1.60 tff(9687,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s19) | node20(s19) | (~until21(s19)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s19) | node20(s19) | (~until21(s19)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9688,plain,
% 1.61/1.60 ((node20(s19) | (~until21(s19)) | xuntil22(s19)) <=> (xuntil22(s19) | node20(s19) | (~until21(s19)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9689,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s19) | (~until21(s19)) | xuntil22(s19))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s19) | node20(s19) | (~until21(s19))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9688])).
% 1.61/1.60 tff(9690,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s19) | (~until21(s19)) | xuntil22(s19))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s19) | node20(s19) | (~until21(s19)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9689, 9687])).
% 1.61/1.60 tff(9691,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s19) | (~until21(s19)) | xuntil22(s19))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9692,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s19) | node20(s19) | (~until21(s19))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9691, 9690])).
% 1.61/1.60 tff(9693,plain,
% 1.61/1.60 (xuntil22(s19)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9692, 9422, 9686, 9253])).
% 1.61/1.60 tff(9694,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s19, s20)) | (~xuntil22(s19)) | until21(s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s19, s20)) | (~xuntil22(s19)) | until21(s20))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9695,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s19, s20)) | (~xuntil22(s19)) | until21(s20))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9696,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s19, s20)) | (~xuntil22(s19)) | until21(s20)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9695, 9694])).
% 1.61/1.60 tff(9697,plain,
% 1.61/1.60 ((~xuntil22(s19)) | until21(s20)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9696, 2004, 9440])).
% 1.61/1.60 tff(9698,plain,
% 1.61/1.60 (until21(s20)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9697, 9693])).
% 1.61/1.60 tff(9699,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s20) | node20(s20) | (~until21(s20)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s20) | node20(s20) | (~until21(s20)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9700,plain,
% 1.61/1.60 ((node20(s20) | (~until21(s20)) | xuntil22(s20)) <=> (xuntil22(s20) | node20(s20) | (~until21(s20)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9701,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s20) | (~until21(s20)) | xuntil22(s20))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s20) | node20(s20) | (~until21(s20))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9700])).
% 1.61/1.60 tff(9702,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s20) | (~until21(s20)) | xuntil22(s20))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s20) | node20(s20) | (~until21(s20)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9701, 9699])).
% 1.61/1.60 tff(9703,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s20) | (~until21(s20)) | xuntil22(s20))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9704,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s20) | node20(s20) | (~until21(s20))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9703, 9702])).
% 1.61/1.60 tff(9705,plain,
% 1.61/1.60 (xuntil22(s20) | node20(s20)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9704, 9422, 9698])).
% 1.61/1.60 tff(9706,plain,
% 1.61/1.60 (xuntil22(s20)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9705, 9245])).
% 1.61/1.60 tff(9707,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s20, s21)) | (~xuntil22(s20)) | until21(s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s20, s21)) | (~xuntil22(s20)) | until21(s21))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9708,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s20, s21)) | (~xuntil22(s20)) | until21(s21))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9709,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s20, s21)) | (~xuntil22(s20)) | until21(s21)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9708, 9707])).
% 1.61/1.60 tff(9710,plain,
% 1.61/1.60 ((~xuntil22(s20)) | until21(s21)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9709, 2065, 9440])).
% 1.61/1.60 tff(9711,plain,
% 1.61/1.60 (until21(s21)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9710, 9706])).
% 1.61/1.60 tff(9712,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s21) | node20(s21) | (~until21(s21)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s21) | node20(s21) | (~until21(s21)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9713,plain,
% 1.61/1.60 ((node20(s21) | (~until21(s21)) | xuntil22(s21)) <=> (xuntil22(s21) | node20(s21) | (~until21(s21)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9714,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s21) | (~until21(s21)) | xuntil22(s21))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s21) | node20(s21) | (~until21(s21))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9713])).
% 1.61/1.60 tff(9715,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s21) | (~until21(s21)) | xuntil22(s21))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s21) | node20(s21) | (~until21(s21)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9714, 9712])).
% 1.61/1.60 tff(9716,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s21) | (~until21(s21)) | xuntil22(s21))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9717,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s21) | node20(s21) | (~until21(s21))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9716, 9715])).
% 1.61/1.60 tff(9718,plain,
% 1.61/1.60 (xuntil22(s21)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9717, 9422, 9711, 9236])).
% 1.61/1.60 tff(9719,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s21, s22)) | (~xuntil22(s21)) | until21(s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s21, s22)) | (~xuntil22(s21)) | until21(s22))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9720,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s21, s22)) | (~xuntil22(s21)) | until21(s22))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9721,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s21, s22)) | (~xuntil22(s21)) | until21(s22)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9720, 9719])).
% 1.61/1.60 tff(9722,plain,
% 1.61/1.60 ((~xuntil22(s21)) | until21(s22)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9721, 2160, 9440])).
% 1.61/1.60 tff(9723,plain,
% 1.61/1.60 (until21(s22)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9722, 9718])).
% 1.61/1.60 tff(9724,plain,
% 1.61/1.60 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s22) | (~node20(s22)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s22) | (~node20(s22)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9725,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s22) | (~node20(s22)))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9726,plain,
% 1.61/1.60 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s22) | (~node20(s22))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9725, 9724])).
% 1.61/1.60 tff(9727,plain,
% 1.61/1.60 (~node20(s22)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9726, 8579, 9227])).
% 1.61/1.60 tff(9728,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s22) | node20(s22) | (~until21(s22)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s22) | node20(s22) | (~until21(s22)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9729,plain,
% 1.61/1.60 ((node20(s22) | (~until21(s22)) | xuntil22(s22)) <=> (xuntil22(s22) | node20(s22) | (~until21(s22)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9730,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s22) | (~until21(s22)) | xuntil22(s22))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s22) | node20(s22) | (~until21(s22))))),
% 1.61/1.60 inference(monotonicity,[status(thm)],[9729])).
% 1.61/1.60 tff(9731,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s22) | (~until21(s22)) | xuntil22(s22))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s22) | node20(s22) | (~until21(s22)))),
% 1.61/1.60 inference(transitivity,[status(thm)],[9730, 9728])).
% 1.61/1.60 tff(9732,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s22) | (~until21(s22)) | xuntil22(s22))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9733,plain,
% 1.61/1.60 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s22) | node20(s22) | (~until21(s22))),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9732, 9731])).
% 1.61/1.60 tff(9734,plain,
% 1.61/1.60 (xuntil22(s22) | (~until21(s22))),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9733, 9422, 9727])).
% 1.61/1.60 tff(9735,plain,
% 1.61/1.60 (xuntil22(s22)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9734, 9723])).
% 1.61/1.60 tff(9736,plain,
% 1.61/1.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s22, s23)) | (~xuntil22(s22)) | until21(s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s22, s23)) | (~xuntil22(s22)) | until21(s23))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9737,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s22, s23)) | (~xuntil22(s22)) | until21(s23))),
% 1.61/1.60 inference(quant_inst,[status(thm)],[])).
% 1.61/1.60 tff(9738,plain,
% 1.61/1.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s22, s23)) | (~xuntil22(s22)) | until21(s23)),
% 1.61/1.60 inference(modus_ponens,[status(thm)],[9737, 9736])).
% 1.61/1.60 tff(9739,plain,
% 1.61/1.60 ((~xuntil22(s22)) | until21(s23)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9738, 2224, 9440])).
% 1.61/1.60 tff(9740,plain,
% 1.61/1.60 (until21(s23)),
% 1.61/1.60 inference(unit_resolution,[status(thm)],[9739, 9735])).
% 1.61/1.60 tff(9741,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s23) | node20(s23) | (~until21(s23)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s23) | node20(s23) | (~until21(s23)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9742,plain,
% 1.61/1.60 ((node20(s23) | (~until21(s23)) | xuntil22(s23)) <=> (xuntil22(s23) | node20(s23) | (~until21(s23)))),
% 1.61/1.60 inference(rewrite,[status(thm)],[])).
% 1.61/1.60 tff(9743,plain,
% 1.61/1.60 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s23) | (~until21(s23)) | xuntil22(s23))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s23) | node20(s23) | (~until21(s23))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9742])).
% 1.61/1.61 tff(9744,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s23) | (~until21(s23)) | xuntil22(s23))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s23) | node20(s23) | (~until21(s23)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9743, 9741])).
% 1.61/1.61 tff(9745,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s23) | (~until21(s23)) | xuntil22(s23))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9746,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s23) | node20(s23) | (~until21(s23))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9745, 9744])).
% 1.61/1.61 tff(9747,plain,
% 1.61/1.61 (xuntil22(s23)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9746, 9422, 9740, 9220])).
% 1.61/1.61 tff(9748,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s23, s24)) | (~xuntil22(s23)) | until21(s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s23, s24)) | (~xuntil22(s23)) | until21(s24))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9749,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s23, s24)) | (~xuntil22(s23)) | until21(s24))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9750,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s23, s24)) | (~xuntil22(s23)) | until21(s24)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9749, 9748])).
% 1.61/1.61 tff(9751,plain,
% 1.61/1.61 ((~xuntil22(s23)) | until21(s24)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9750, 2299, 9440])).
% 1.61/1.61 tff(9752,plain,
% 1.61/1.61 (until21(s24)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9751, 9747])).
% 1.61/1.61 tff(9753,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s24) | node20(s24) | (~until21(s24)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s24) | node20(s24) | (~until21(s24)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9754,plain,
% 1.61/1.61 ((node20(s24) | (~until21(s24)) | xuntil22(s24)) <=> (xuntil22(s24) | node20(s24) | (~until21(s24)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9755,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s24) | (~until21(s24)) | xuntil22(s24))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s24) | node20(s24) | (~until21(s24))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9754])).
% 1.61/1.61 tff(9756,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s24) | (~until21(s24)) | xuntil22(s24))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s24) | node20(s24) | (~until21(s24)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9755, 9753])).
% 1.61/1.61 tff(9757,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s24) | (~until21(s24)) | xuntil22(s24))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9758,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s24) | node20(s24) | (~until21(s24))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9757, 9756])).
% 1.61/1.61 tff(9759,plain,
% 1.61/1.61 (xuntil22(s24) | node20(s24)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9758, 9422, 9752])).
% 1.61/1.61 tff(9760,plain,
% 1.61/1.61 (xuntil22(s24)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9759, 9212])).
% 1.61/1.61 tff(9761,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s24, s25)) | (~xuntil22(s24)) | until21(s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s24, s25)) | (~xuntil22(s24)) | until21(s25))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9762,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s24, s25)) | (~xuntil22(s24)) | until21(s25))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9763,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s24, s25)) | (~xuntil22(s24)) | until21(s25)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9762, 9761])).
% 1.61/1.61 tff(9764,plain,
% 1.61/1.61 ((~xuntil22(s24)) | until21(s25)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9763, 2388, 9440])).
% 1.61/1.61 tff(9765,plain,
% 1.61/1.61 (until21(s25)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9764, 9760])).
% 1.61/1.61 tff(9766,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s25) | node20(s25) | (~until21(s25)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s25) | node20(s25) | (~until21(s25)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9767,plain,
% 1.61/1.61 ((node20(s25) | (~until21(s25)) | xuntil22(s25)) <=> (xuntil22(s25) | node20(s25) | (~until21(s25)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9768,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s25) | (~until21(s25)) | xuntil22(s25))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s25) | node20(s25) | (~until21(s25))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9767])).
% 1.61/1.61 tff(9769,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s25) | (~until21(s25)) | xuntil22(s25))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s25) | node20(s25) | (~until21(s25)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9768, 9766])).
% 1.61/1.61 tff(9770,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s25) | (~until21(s25)) | xuntil22(s25))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9771,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s25) | node20(s25) | (~until21(s25))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9770, 9769])).
% 1.61/1.61 tff(9772,plain,
% 1.61/1.61 (xuntil22(s25)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9771, 9422, 9765, 9203])).
% 1.61/1.61 tff(9773,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s25, s26)) | (~xuntil22(s25)) | until21(s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s25, s26)) | (~xuntil22(s25)) | until21(s26))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9774,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s25, s26)) | (~xuntil22(s25)) | until21(s26))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9775,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s25, s26)) | (~xuntil22(s25)) | until21(s26)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9774, 9773])).
% 1.61/1.61 tff(9776,plain,
% 1.61/1.61 ((~xuntil22(s25)) | until21(s26)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9775, 2455, 9440])).
% 1.61/1.61 tff(9777,plain,
% 1.61/1.61 (until21(s26)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9776, 9772])).
% 1.61/1.61 tff(9778,plain,
% 1.61/1.61 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s26) | (~node20(s26)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s26) | (~node20(s26)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9779,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s26) | (~node20(s26)))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9780,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s26) | (~node20(s26))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9779, 9778])).
% 1.61/1.61 tff(9781,plain,
% 1.61/1.61 (~node20(s26)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9780, 8579, 9194])).
% 1.61/1.61 tff(9782,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s26) | node20(s26) | (~until21(s26)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s26) | node20(s26) | (~until21(s26)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9783,plain,
% 1.61/1.61 ((node20(s26) | (~until21(s26)) | xuntil22(s26)) <=> (xuntil22(s26) | node20(s26) | (~until21(s26)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9784,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s26) | (~until21(s26)) | xuntil22(s26))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s26) | node20(s26) | (~until21(s26))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9783])).
% 1.61/1.61 tff(9785,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s26) | (~until21(s26)) | xuntil22(s26))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s26) | node20(s26) | (~until21(s26)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9784, 9782])).
% 1.61/1.61 tff(9786,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s26) | (~until21(s26)) | xuntil22(s26))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9787,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s26) | node20(s26) | (~until21(s26))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9786, 9785])).
% 1.61/1.61 tff(9788,plain,
% 1.61/1.61 (xuntil22(s26) | (~until21(s26))),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9787, 9422, 9781])).
% 1.61/1.61 tff(9789,plain,
% 1.61/1.61 (xuntil22(s26)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9788, 9777])).
% 1.61/1.61 tff(9790,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s26, s27)) | (~xuntil22(s26)) | until21(s27))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s26, s27)) | (~xuntil22(s26)) | until21(s27))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9791,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s26, s27)) | (~xuntil22(s26)) | until21(s27))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9792,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s26, s27)) | (~xuntil22(s26)) | until21(s27)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9791, 9790])).
% 1.61/1.61 tff(9793,plain,
% 1.61/1.61 ((~xuntil22(s26)) | until21(s27)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9792, 2554, 9440])).
% 1.61/1.61 tff(9794,plain,
% 1.61/1.61 (until21(s27)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9793, 9789])).
% 1.61/1.61 tff(9795,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s27) | node20(s27) | (~until21(s27)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s27) | node20(s27) | (~until21(s27)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9796,plain,
% 1.61/1.61 ((node20(s27) | (~until21(s27)) | xuntil22(s27)) <=> (xuntil22(s27) | node20(s27) | (~until21(s27)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9797,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s27) | (~until21(s27)) | xuntil22(s27))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s27) | node20(s27) | (~until21(s27))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9796])).
% 1.61/1.61 tff(9798,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s27) | (~until21(s27)) | xuntil22(s27))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s27) | node20(s27) | (~until21(s27)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9797, 9795])).
% 1.61/1.61 tff(9799,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s27) | (~until21(s27)) | xuntil22(s27))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9800,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s27) | node20(s27) | (~until21(s27))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9799, 9798])).
% 1.61/1.61 tff(9801,plain,
% 1.61/1.61 (xuntil22(s27)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9800, 9422, 9794, 9187])).
% 1.61/1.61 tff(9802,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s27, s28)) | (~xuntil22(s27)) | until21(s28))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s27, s28)) | (~xuntil22(s27)) | until21(s28))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9803,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s27, s28)) | (~xuntil22(s27)) | until21(s28))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9804,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s27, s28)) | (~xuntil22(s27)) | until21(s28)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9803, 9802])).
% 1.61/1.61 tff(9805,plain,
% 1.61/1.61 ((~xuntil22(s27)) | until21(s28)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9804, 2632, 9440])).
% 1.61/1.61 tff(9806,plain,
% 1.61/1.61 (until21(s28)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9805, 9801])).
% 1.61/1.61 tff(9807,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s28) | node20(s28) | (~until21(s28)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s28) | node20(s28) | (~until21(s28)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9808,plain,
% 1.61/1.61 ((node20(s28) | (~until21(s28)) | xuntil22(s28)) <=> (xuntil22(s28) | node20(s28) | (~until21(s28)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9809,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s28) | (~until21(s28)) | xuntil22(s28))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s28) | node20(s28) | (~until21(s28))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9808])).
% 1.61/1.61 tff(9810,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s28) | (~until21(s28)) | xuntil22(s28))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s28) | node20(s28) | (~until21(s28)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9809, 9807])).
% 1.61/1.61 tff(9811,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s28) | (~until21(s28)) | xuntil22(s28))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9812,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s28) | node20(s28) | (~until21(s28))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9811, 9810])).
% 1.61/1.61 tff(9813,plain,
% 1.61/1.61 (xuntil22(s28) | node20(s28)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9812, 9422, 9806])).
% 1.61/1.61 tff(9814,plain,
% 1.61/1.61 (xuntil22(s28)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9813, 9179])).
% 1.61/1.61 tff(9815,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s28, s29)) | (~xuntil22(s28)) | until21(s29))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s28, s29)) | (~xuntil22(s28)) | until21(s29))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9816,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s28, s29)) | (~xuntil22(s28)) | until21(s29))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9817,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s28, s29)) | (~xuntil22(s28)) | until21(s29)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9816, 9815])).
% 1.61/1.61 tff(9818,plain,
% 1.61/1.61 ((~xuntil22(s28)) | until21(s29)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9817, 2693, 9440])).
% 1.61/1.61 tff(9819,plain,
% 1.61/1.61 (until21(s29)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9818, 9814])).
% 1.61/1.61 tff(9820,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s29) | node20(s29) | (~until21(s29)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s29) | node20(s29) | (~until21(s29)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9821,plain,
% 1.61/1.61 ((node20(s29) | (~until21(s29)) | xuntil22(s29)) <=> (xuntil22(s29) | node20(s29) | (~until21(s29)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9822,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s29) | (~until21(s29)) | xuntil22(s29))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s29) | node20(s29) | (~until21(s29))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9821])).
% 1.61/1.61 tff(9823,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s29) | (~until21(s29)) | xuntil22(s29))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s29) | node20(s29) | (~until21(s29)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9822, 9820])).
% 1.61/1.61 tff(9824,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s29) | (~until21(s29)) | xuntil22(s29))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9825,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s29) | node20(s29) | (~until21(s29))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9824, 9823])).
% 1.61/1.61 tff(9826,plain,
% 1.61/1.61 (xuntil22(s29)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9825, 9422, 9819, 9170])).
% 1.61/1.61 tff(9827,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s29, s30)) | (~xuntil22(s29)) | until21(s30))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s29, s30)) | (~xuntil22(s29)) | until21(s30))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9828,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s29, s30)) | (~xuntil22(s29)) | until21(s30))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9829,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s29, s30)) | (~xuntil22(s29)) | until21(s30)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9828, 9827])).
% 1.61/1.61 tff(9830,plain,
% 1.61/1.61 ((~xuntil22(s29)) | until21(s30)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9829, 2788, 9440])).
% 1.61/1.61 tff(9831,plain,
% 1.61/1.61 (until21(s30)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9830, 9826])).
% 1.61/1.61 tff(9832,plain,
% 1.61/1.61 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s30) | (~node20(s30)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s30) | (~node20(s30)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9833,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s30) | (~node20(s30)))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9834,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s30) | (~node20(s30))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9833, 9832])).
% 1.61/1.61 tff(9835,plain,
% 1.61/1.61 (~node20(s30)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9834, 8579, 9161])).
% 1.61/1.61 tff(9836,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s30) | node20(s30) | (~until21(s30)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s30) | node20(s30) | (~until21(s30)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9837,plain,
% 1.61/1.61 ((node20(s30) | (~until21(s30)) | xuntil22(s30)) <=> (xuntil22(s30) | node20(s30) | (~until21(s30)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9838,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s30) | (~until21(s30)) | xuntil22(s30))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s30) | node20(s30) | (~until21(s30))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9837])).
% 1.61/1.61 tff(9839,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s30) | (~until21(s30)) | xuntil22(s30))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s30) | node20(s30) | (~until21(s30)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9838, 9836])).
% 1.61/1.61 tff(9840,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s30) | (~until21(s30)) | xuntil22(s30))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9841,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s30) | node20(s30) | (~until21(s30))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 1.61/1.61 tff(9842,plain,
% 1.61/1.61 (xuntil22(s30) | (~until21(s30))),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9841, 9422, 9835])).
% 1.61/1.61 tff(9843,plain,
% 1.61/1.61 (xuntil22(s30)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9842, 9831])).
% 1.61/1.61 tff(9844,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s30, s31)) | (~xuntil22(s30)) | until21(s31))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s30, s31)) | (~xuntil22(s30)) | until21(s31))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9845,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s30, s31)) | (~xuntil22(s30)) | until21(s31))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9846,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s30, s31)) | (~xuntil22(s30)) | until21(s31)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9845, 9844])).
% 1.61/1.61 tff(9847,plain,
% 1.61/1.61 ((~xuntil22(s30)) | until21(s31)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9846, 2852, 9440])).
% 1.61/1.61 tff(9848,plain,
% 1.61/1.61 (until21(s31)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9847, 9843])).
% 1.61/1.61 tff(9849,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s31) | node20(s31) | (~until21(s31)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s31) | node20(s31) | (~until21(s31)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9850,plain,
% 1.61/1.61 ((node20(s31) | (~until21(s31)) | xuntil22(s31)) <=> (xuntil22(s31) | node20(s31) | (~until21(s31)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9851,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s31) | (~until21(s31)) | xuntil22(s31))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s31) | node20(s31) | (~until21(s31))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9850])).
% 1.61/1.61 tff(9852,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s31) | (~until21(s31)) | xuntil22(s31))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s31) | node20(s31) | (~until21(s31)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9851, 9849])).
% 1.61/1.61 tff(9853,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s31) | (~until21(s31)) | xuntil22(s31))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9854,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s31) | node20(s31) | (~until21(s31))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9853, 9852])).
% 1.61/1.61 tff(9855,plain,
% 1.61/1.61 (xuntil22(s31)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9854, 9422, 9848, 9154])).
% 1.61/1.61 tff(9856,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s31, s32)) | (~xuntil22(s31)) | until21(s32))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s31, s32)) | (~xuntil22(s31)) | until21(s32))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9857,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s31, s32)) | (~xuntil22(s31)) | until21(s32))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9858,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s31, s32)) | (~xuntil22(s31)) | until21(s32)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9857, 9856])).
% 1.61/1.61 tff(9859,plain,
% 1.61/1.61 ((~xuntil22(s31)) | until21(s32)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9858, 2927, 9440])).
% 1.61/1.61 tff(9860,plain,
% 1.61/1.61 (until21(s32)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9859, 9855])).
% 1.61/1.61 tff(9861,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s32) | node20(s32) | (~until21(s32)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s32) | node20(s32) | (~until21(s32)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9862,plain,
% 1.61/1.61 ((node20(s32) | (~until21(s32)) | xuntil22(s32)) <=> (xuntil22(s32) | node20(s32) | (~until21(s32)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9863,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s32) | (~until21(s32)) | xuntil22(s32))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s32) | node20(s32) | (~until21(s32))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9862])).
% 1.61/1.61 tff(9864,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s32) | (~until21(s32)) | xuntil22(s32))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s32) | node20(s32) | (~until21(s32)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9863, 9861])).
% 1.61/1.61 tff(9865,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s32) | (~until21(s32)) | xuntil22(s32))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9866,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s32) | node20(s32) | (~until21(s32))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9865, 9864])).
% 1.61/1.61 tff(9867,plain,
% 1.61/1.61 (xuntil22(s32) | node20(s32)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9866, 9422, 9860])).
% 1.61/1.61 tff(9868,plain,
% 1.61/1.61 (xuntil22(s32)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9867, 9146])).
% 1.61/1.61 tff(9869,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s32, s33)) | (~xuntil22(s32)) | until21(s33))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s32, s33)) | (~xuntil22(s32)) | until21(s33))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9870,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s32, s33)) | (~xuntil22(s32)) | until21(s33))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9871,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s32, s33)) | (~xuntil22(s32)) | until21(s33)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9870, 9869])).
% 1.61/1.61 tff(9872,plain,
% 1.61/1.61 ((~xuntil22(s32)) | until21(s33)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9871, 3016, 9440])).
% 1.61/1.61 tff(9873,plain,
% 1.61/1.61 (until21(s33)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9872, 9868])).
% 1.61/1.61 tff(9874,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s33) | node20(s33) | (~until21(s33)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s33) | node20(s33) | (~until21(s33)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9875,plain,
% 1.61/1.61 ((node20(s33) | (~until21(s33)) | xuntil22(s33)) <=> (xuntil22(s33) | node20(s33) | (~until21(s33)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9876,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s33) | (~until21(s33)) | xuntil22(s33))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s33) | node20(s33) | (~until21(s33))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9875])).
% 1.61/1.61 tff(9877,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s33) | (~until21(s33)) | xuntil22(s33))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s33) | node20(s33) | (~until21(s33)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9876, 9874])).
% 1.61/1.61 tff(9878,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s33) | (~until21(s33)) | xuntil22(s33))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9879,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s33) | node20(s33) | (~until21(s33))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9878, 9877])).
% 1.61/1.61 tff(9880,plain,
% 1.61/1.61 (xuntil22(s33)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9879, 9422, 9873, 9137])).
% 1.61/1.61 tff(9881,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s33, s34)) | (~xuntil22(s33)) | until21(s34))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s33, s34)) | (~xuntil22(s33)) | until21(s34))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9882,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s33, s34)) | (~xuntil22(s33)) | until21(s34))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9883,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s33, s34)) | (~xuntil22(s33)) | until21(s34)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9882, 9881])).
% 1.61/1.61 tff(9884,plain,
% 1.61/1.61 ((~xuntil22(s33)) | until21(s34)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9883, 3083, 9440])).
% 1.61/1.61 tff(9885,plain,
% 1.61/1.61 (until21(s34)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9884, 9880])).
% 1.61/1.61 tff(9886,plain,
% 1.61/1.61 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s34) | (~node20(s34)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s34) | (~node20(s34)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9887,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s34) | (~node20(s34)))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9888,plain,
% 1.61/1.61 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s34) | (~node20(s34))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9887, 9886])).
% 1.61/1.61 tff(9889,plain,
% 1.61/1.61 (~node20(s34)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9888, 8579, 9128])).
% 1.61/1.61 tff(9890,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s34) | node20(s34) | (~until21(s34)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s34) | node20(s34) | (~until21(s34)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9891,plain,
% 1.61/1.61 ((node20(s34) | (~until21(s34)) | xuntil22(s34)) <=> (xuntil22(s34) | node20(s34) | (~until21(s34)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9892,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s34) | (~until21(s34)) | xuntil22(s34))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s34) | node20(s34) | (~until21(s34))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9891])).
% 1.61/1.61 tff(9893,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s34) | (~until21(s34)) | xuntil22(s34))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s34) | node20(s34) | (~until21(s34)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9892, 9890])).
% 1.61/1.61 tff(9894,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s34) | (~until21(s34)) | xuntil22(s34))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9895,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s34) | node20(s34) | (~until21(s34))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9894, 9893])).
% 1.61/1.61 tff(9896,plain,
% 1.61/1.61 (xuntil22(s34) | (~until21(s34))),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9895, 9422, 9889])).
% 1.61/1.61 tff(9897,plain,
% 1.61/1.61 (xuntil22(s34)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9896, 9885])).
% 1.61/1.61 tff(9898,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s34, s35)) | (~xuntil22(s34)) | until21(s35))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s34, s35)) | (~xuntil22(s34)) | until21(s35))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9899,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s34, s35)) | (~xuntil22(s34)) | until21(s35))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9900,plain,
% 1.61/1.61 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s34, s35)) | (~xuntil22(s34)) | until21(s35)),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9899, 9898])).
% 1.61/1.61 tff(9901,plain,
% 1.61/1.61 ((~xuntil22(s34)) | until21(s35)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9900, 3182, 9440])).
% 1.61/1.61 tff(9902,plain,
% 1.61/1.61 (until21(s35)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9901, 9897])).
% 1.61/1.61 tff(9903,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s35) | node20(s35) | (~until21(s35)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s35) | node20(s35) | (~until21(s35)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9904,plain,
% 1.61/1.61 ((node20(s35) | (~until21(s35)) | xuntil22(s35)) <=> (xuntil22(s35) | node20(s35) | (~until21(s35)))),
% 1.61/1.61 inference(rewrite,[status(thm)],[])).
% 1.61/1.61 tff(9905,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s35) | (~until21(s35)) | xuntil22(s35))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s35) | node20(s35) | (~until21(s35))))),
% 1.61/1.61 inference(monotonicity,[status(thm)],[9904])).
% 1.61/1.61 tff(9906,plain,
% 1.61/1.61 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s35) | (~until21(s35)) | xuntil22(s35))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s35) | node20(s35) | (~until21(s35)))),
% 1.61/1.61 inference(transitivity,[status(thm)],[9905, 9903])).
% 1.61/1.61 tff(9907,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s35) | (~until21(s35)) | xuntil22(s35))),
% 1.61/1.61 inference(quant_inst,[status(thm)],[])).
% 1.61/1.61 tff(9908,plain,
% 1.61/1.61 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s35) | node20(s35) | (~until21(s35))),
% 1.61/1.61 inference(modus_ponens,[status(thm)],[9907, 9906])).
% 1.61/1.61 tff(9909,plain,
% 1.61/1.61 (xuntil22(s35)),
% 1.61/1.61 inference(unit_resolution,[status(thm)],[9908, 9422, 9902, 9121])).
% 1.61/1.61 tff(9910,plain,
% 1.61/1.61 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s35, s36)) | (~xuntil22(s35)) | until21(s36))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s35, s36)) | (~xuntil22(s35)) | until21(s36))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9911,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s35, s36)) | (~xuntil22(s35)) | until21(s36))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9912,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s35, s36)) | (~xuntil22(s35)) | until21(s36)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9911, 9910])).
% 1.61/1.62 tff(9913,plain,
% 1.61/1.62 ((~xuntil22(s35)) | until21(s36)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9912, 3260, 9440])).
% 1.61/1.62 tff(9914,plain,
% 1.61/1.62 (until21(s36)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9913, 9909])).
% 1.61/1.62 tff(9915,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s36) | node20(s36) | (~until21(s36)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s36) | node20(s36) | (~until21(s36)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9916,plain,
% 1.61/1.62 ((node20(s36) | (~until21(s36)) | xuntil22(s36)) <=> (xuntil22(s36) | node20(s36) | (~until21(s36)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9917,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s36) | (~until21(s36)) | xuntil22(s36))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s36) | node20(s36) | (~until21(s36))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9916])).
% 1.61/1.62 tff(9918,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s36) | (~until21(s36)) | xuntil22(s36))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s36) | node20(s36) | (~until21(s36)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9917, 9915])).
% 1.61/1.62 tff(9919,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s36) | (~until21(s36)) | xuntil22(s36))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9920,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s36) | node20(s36) | (~until21(s36))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9919, 9918])).
% 1.61/1.62 tff(9921,plain,
% 1.61/1.62 (xuntil22(s36) | node20(s36)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9920, 9422, 9914])).
% 1.61/1.62 tff(9922,plain,
% 1.61/1.62 (xuntil22(s36)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9921, 9113])).
% 1.61/1.62 tff(9923,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s36, s37)) | (~xuntil22(s36)) | until21(s37))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s36, s37)) | (~xuntil22(s36)) | until21(s37))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9924,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s36, s37)) | (~xuntil22(s36)) | until21(s37))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9925,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s36, s37)) | (~xuntil22(s36)) | until21(s37)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9924, 9923])).
% 1.61/1.62 tff(9926,plain,
% 1.61/1.62 ((~xuntil22(s36)) | until21(s37)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9925, 3321, 9440])).
% 1.61/1.62 tff(9927,plain,
% 1.61/1.62 (until21(s37)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9926, 9922])).
% 1.61/1.62 tff(9928,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s37) | node20(s37) | (~until21(s37)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s37) | node20(s37) | (~until21(s37)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9929,plain,
% 1.61/1.62 ((node20(s37) | (~until21(s37)) | xuntil22(s37)) <=> (xuntil22(s37) | node20(s37) | (~until21(s37)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9930,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s37) | (~until21(s37)) | xuntil22(s37))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s37) | node20(s37) | (~until21(s37))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9929])).
% 1.61/1.62 tff(9931,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s37) | (~until21(s37)) | xuntil22(s37))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s37) | node20(s37) | (~until21(s37)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9930, 9928])).
% 1.61/1.62 tff(9932,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s37) | (~until21(s37)) | xuntil22(s37))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9933,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s37) | node20(s37) | (~until21(s37))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9932, 9931])).
% 1.61/1.62 tff(9934,plain,
% 1.61/1.62 (xuntil22(s37)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9933, 9422, 9927, 9104])).
% 1.61/1.62 tff(9935,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s37, s38)) | (~xuntil22(s37)) | until21(s38))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s37, s38)) | (~xuntil22(s37)) | until21(s38))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9936,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s37, s38)) | (~xuntil22(s37)) | until21(s38))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9937,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s37, s38)) | (~xuntil22(s37)) | until21(s38)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9936, 9935])).
% 1.61/1.62 tff(9938,plain,
% 1.61/1.62 ((~xuntil22(s37)) | until21(s38)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9937, 3416, 9440])).
% 1.61/1.62 tff(9939,plain,
% 1.61/1.62 (until21(s38)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9938, 9934])).
% 1.61/1.62 tff(9940,plain,
% 1.61/1.62 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s38) | (~node20(s38)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s38) | (~node20(s38)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9941,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s38) | (~node20(s38)))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9942,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s38) | (~node20(s38))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9941, 9940])).
% 1.61/1.62 tff(9943,plain,
% 1.61/1.62 (~node20(s38)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9942, 8579, 3446])).
% 1.61/1.62 tff(9944,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s38) | node20(s38) | (~until21(s38)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s38) | node20(s38) | (~until21(s38)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9945,plain,
% 1.61/1.62 ((node20(s38) | (~until21(s38)) | xuntil22(s38)) <=> (xuntil22(s38) | node20(s38) | (~until21(s38)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9946,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s38) | (~until21(s38)) | xuntil22(s38))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s38) | node20(s38) | (~until21(s38))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9945])).
% 1.61/1.62 tff(9947,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s38) | (~until21(s38)) | xuntil22(s38))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s38) | node20(s38) | (~until21(s38)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9946, 9944])).
% 1.61/1.62 tff(9948,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s38) | (~until21(s38)) | xuntil22(s38))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9949,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s38) | node20(s38) | (~until21(s38))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9948, 9947])).
% 1.61/1.62 tff(9950,plain,
% 1.61/1.62 (xuntil22(s38) | (~until21(s38))),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9949, 9422, 9943])).
% 1.61/1.62 tff(9951,plain,
% 1.61/1.62 (xuntil22(s38)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9950, 9939])).
% 1.61/1.62 tff(9952,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s38, s39)) | (~xuntil22(s38)) | until21(s39))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s38, s39)) | (~xuntil22(s38)) | until21(s39))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9953,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s38, s39)) | (~xuntil22(s38)) | until21(s39))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9954,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s38, s39)) | (~xuntil22(s38)) | until21(s39)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9953, 9952])).
% 1.61/1.62 tff(9955,plain,
% 1.61/1.62 ((~xuntil22(s38)) | until21(s39)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9954, 3495, 9440])).
% 1.61/1.62 tff(9956,plain,
% 1.61/1.62 (until21(s39)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9955, 9951])).
% 1.61/1.62 tff(9957,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s39) | node20(s39) | (~until21(s39)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s39) | node20(s39) | (~until21(s39)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9958,plain,
% 1.61/1.62 ((node20(s39) | (~until21(s39)) | xuntil22(s39)) <=> (xuntil22(s39) | node20(s39) | (~until21(s39)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9959,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s39) | (~until21(s39)) | xuntil22(s39))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s39) | node20(s39) | (~until21(s39))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9958])).
% 1.61/1.62 tff(9960,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s39) | (~until21(s39)) | xuntil22(s39))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s39) | node20(s39) | (~until21(s39)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9959, 9957])).
% 1.61/1.62 tff(9961,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s39) | (~until21(s39)) | xuntil22(s39))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9962,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s39) | node20(s39) | (~until21(s39))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9961, 9960])).
% 1.61/1.62 tff(9963,plain,
% 1.61/1.62 (xuntil22(s39)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9962, 9422, 9956, 9095])).
% 1.61/1.62 tff(9964,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s39, s40)) | (~xuntil22(s39)) | until21(s40))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s39, s40)) | (~xuntil22(s39)) | until21(s40))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9965,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s39, s40)) | (~xuntil22(s39)) | until21(s40))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9966,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s39, s40)) | (~xuntil22(s39)) | until21(s40)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9965, 9964])).
% 1.61/1.62 tff(9967,plain,
% 1.61/1.62 ((~xuntil22(s39)) | until21(s40)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9966, 3570, 9440])).
% 1.61/1.62 tff(9968,plain,
% 1.61/1.62 (until21(s40)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9967, 9963])).
% 1.61/1.62 tff(9969,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s40) | node20(s40) | (~until21(s40)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s40) | node20(s40) | (~until21(s40)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9970,plain,
% 1.61/1.62 ((node20(s40) | (~until21(s40)) | xuntil22(s40)) <=> (xuntil22(s40) | node20(s40) | (~until21(s40)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9971,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s40) | (~until21(s40)) | xuntil22(s40))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s40) | node20(s40) | (~until21(s40))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9970])).
% 1.61/1.62 tff(9972,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s40) | (~until21(s40)) | xuntil22(s40))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s40) | node20(s40) | (~until21(s40)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9971, 9969])).
% 1.61/1.62 tff(9973,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s40) | (~until21(s40)) | xuntil22(s40))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9974,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s40) | node20(s40) | (~until21(s40))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9973, 9972])).
% 1.61/1.62 tff(9975,plain,
% 1.61/1.62 (xuntil22(s40) | node20(s40)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9974, 9422, 9968])).
% 1.61/1.62 tff(9976,plain,
% 1.61/1.62 (xuntil22(s40)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9975, 9087])).
% 1.61/1.62 tff(9977,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s40, s41)) | (~xuntil22(s40)) | until21(s41))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s40, s41)) | (~xuntil22(s40)) | until21(s41))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9978,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s40, s41)) | (~xuntil22(s40)) | until21(s41))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9979,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s40, s41)) | (~xuntil22(s40)) | until21(s41)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9978, 9977])).
% 1.61/1.62 tff(9980,plain,
% 1.61/1.62 ((~xuntil22(s40)) | until21(s41)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9979, 3659, 9440])).
% 1.61/1.62 tff(9981,plain,
% 1.61/1.62 (until21(s41)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9980, 9976])).
% 1.61/1.62 tff(9982,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s41) | node20(s41) | (~until21(s41)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s41) | node20(s41) | (~until21(s41)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9983,plain,
% 1.61/1.62 ((node20(s41) | (~until21(s41)) | xuntil22(s41)) <=> (xuntil22(s41) | node20(s41) | (~until21(s41)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9984,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s41) | (~until21(s41)) | xuntil22(s41))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s41) | node20(s41) | (~until21(s41))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9983])).
% 1.61/1.62 tff(9985,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s41) | (~until21(s41)) | xuntil22(s41))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s41) | node20(s41) | (~until21(s41)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[9984, 9982])).
% 1.61/1.62 tff(9986,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s41) | (~until21(s41)) | xuntil22(s41))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9987,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s41) | node20(s41) | (~until21(s41))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9986, 9985])).
% 1.61/1.62 tff(9988,plain,
% 1.61/1.62 (xuntil22(s41)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9987, 9422, 9981, 9078])).
% 1.61/1.62 tff(9989,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s41, s42)) | (~xuntil22(s41)) | until21(s42))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s41, s42)) | (~xuntil22(s41)) | until21(s42))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9990,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s41, s42)) | (~xuntil22(s41)) | until21(s42))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9991,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s41, s42)) | (~xuntil22(s41)) | until21(s42)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9990, 9989])).
% 1.61/1.62 tff(9992,plain,
% 1.61/1.62 ((~xuntil22(s41)) | until21(s42)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9991, 3726, 9440])).
% 1.61/1.62 tff(9993,plain,
% 1.61/1.62 (until21(s42)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9992, 9988])).
% 1.61/1.62 tff(9994,plain,
% 1.61/1.62 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s42) | (~node20(s42)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s42) | (~node20(s42)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9995,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s42) | (~node20(s42)))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(9996,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s42) | (~node20(s42))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[9995, 9994])).
% 1.61/1.62 tff(9997,plain,
% 1.61/1.62 (~node20(s42)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[9996, 8579, 9069])).
% 1.61/1.62 tff(9998,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s42) | node20(s42) | (~until21(s42)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s42) | node20(s42) | (~until21(s42)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(9999,plain,
% 1.61/1.62 ((node20(s42) | (~until21(s42)) | xuntil22(s42)) <=> (xuntil22(s42) | node20(s42) | (~until21(s42)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10000,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s42) | (~until21(s42)) | xuntil22(s42))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s42) | node20(s42) | (~until21(s42))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[9999])).
% 1.61/1.62 tff(10001,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s42) | (~until21(s42)) | xuntil22(s42))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s42) | node20(s42) | (~until21(s42)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10000, 9998])).
% 1.61/1.62 tff(10002,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s42) | (~until21(s42)) | xuntil22(s42))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10003,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s42) | node20(s42) | (~until21(s42))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10002, 10001])).
% 1.61/1.62 tff(10004,plain,
% 1.61/1.62 (xuntil22(s42) | (~until21(s42))),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10003, 9422, 9997])).
% 1.61/1.62 tff(10005,plain,
% 1.61/1.62 (xuntil22(s42)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10004, 9993])).
% 1.61/1.62 tff(10006,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s42, s43)) | (~xuntil22(s42)) | until21(s43))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s42, s43)) | (~xuntil22(s42)) | until21(s43))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10007,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s42, s43)) | (~xuntil22(s42)) | until21(s43))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10008,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s42, s43)) | (~xuntil22(s42)) | until21(s43)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10007, 10006])).
% 1.61/1.62 tff(10009,plain,
% 1.61/1.62 ((~xuntil22(s42)) | until21(s43)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10008, 3825, 9440])).
% 1.61/1.62 tff(10010,plain,
% 1.61/1.62 (until21(s43)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10009, 10005])).
% 1.61/1.62 tff(10011,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s43) | node20(s43) | (~until21(s43)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s43) | node20(s43) | (~until21(s43)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10012,plain,
% 1.61/1.62 ((node20(s43) | (~until21(s43)) | xuntil22(s43)) <=> (xuntil22(s43) | node20(s43) | (~until21(s43)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10013,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s43) | (~until21(s43)) | xuntil22(s43))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s43) | node20(s43) | (~until21(s43))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10012])).
% 1.61/1.62 tff(10014,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s43) | (~until21(s43)) | xuntil22(s43))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s43) | node20(s43) | (~until21(s43)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10013, 10011])).
% 1.61/1.62 tff(10015,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s43) | (~until21(s43)) | xuntil22(s43))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10016,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s43) | node20(s43) | (~until21(s43))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10015, 10014])).
% 1.61/1.62 tff(10017,plain,
% 1.61/1.62 (xuntil22(s43)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10016, 9422, 10010, 9062])).
% 1.61/1.62 tff(10018,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s43, s44)) | (~xuntil22(s43)) | until21(s44))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s43, s44)) | (~xuntil22(s43)) | until21(s44))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10019,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s43, s44)) | (~xuntil22(s43)) | until21(s44))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10020,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s43, s44)) | (~xuntil22(s43)) | until21(s44)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10019, 10018])).
% 1.61/1.62 tff(10021,plain,
% 1.61/1.62 ((~xuntil22(s43)) | until21(s44)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10020, 3903, 9440])).
% 1.61/1.62 tff(10022,plain,
% 1.61/1.62 (until21(s44)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10021, 10017])).
% 1.61/1.62 tff(10023,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s44) | node20(s44) | (~until21(s44)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s44) | node20(s44) | (~until21(s44)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10024,plain,
% 1.61/1.62 ((node20(s44) | (~until21(s44)) | xuntil22(s44)) <=> (xuntil22(s44) | node20(s44) | (~until21(s44)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10025,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s44) | (~until21(s44)) | xuntil22(s44))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s44) | node20(s44) | (~until21(s44))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10024])).
% 1.61/1.62 tff(10026,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s44) | (~until21(s44)) | xuntil22(s44))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s44) | node20(s44) | (~until21(s44)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10025, 10023])).
% 1.61/1.62 tff(10027,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s44) | (~until21(s44)) | xuntil22(s44))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10028,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s44) | node20(s44) | (~until21(s44))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10027, 10026])).
% 1.61/1.62 tff(10029,plain,
% 1.61/1.62 (xuntil22(s44) | node20(s44)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10028, 9422, 10022])).
% 1.61/1.62 tff(10030,plain,
% 1.61/1.62 (xuntil22(s44)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10029, 9054])).
% 1.61/1.62 tff(10031,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s44, s45)) | (~xuntil22(s44)) | until21(s45))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s44, s45)) | (~xuntil22(s44)) | until21(s45))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10032,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s44, s45)) | (~xuntil22(s44)) | until21(s45))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10033,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s44, s45)) | (~xuntil22(s44)) | until21(s45)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10032, 10031])).
% 1.61/1.62 tff(10034,plain,
% 1.61/1.62 ((~xuntil22(s44)) | until21(s45)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10033, 3964, 9440])).
% 1.61/1.62 tff(10035,plain,
% 1.61/1.62 (until21(s45)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10034, 10030])).
% 1.61/1.62 tff(10036,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s45) | node20(s45) | (~until21(s45)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s45) | node20(s45) | (~until21(s45)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10037,plain,
% 1.61/1.62 ((node20(s45) | (~until21(s45)) | xuntil22(s45)) <=> (xuntil22(s45) | node20(s45) | (~until21(s45)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10038,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s45) | (~until21(s45)) | xuntil22(s45))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s45) | node20(s45) | (~until21(s45))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10037])).
% 1.61/1.62 tff(10039,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s45) | (~until21(s45)) | xuntil22(s45))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s45) | node20(s45) | (~until21(s45)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10038, 10036])).
% 1.61/1.62 tff(10040,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s45) | (~until21(s45)) | xuntil22(s45))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10041,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s45) | node20(s45) | (~until21(s45))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10040, 10039])).
% 1.61/1.62 tff(10042,plain,
% 1.61/1.62 (xuntil22(s45)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10041, 9422, 10035, 9045])).
% 1.61/1.62 tff(10043,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s45, s46)) | (~xuntil22(s45)) | until21(s46))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s45, s46)) | (~xuntil22(s45)) | until21(s46))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10044,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s45, s46)) | (~xuntil22(s45)) | until21(s46))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10045,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s45, s46)) | (~xuntil22(s45)) | until21(s46)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10044, 10043])).
% 1.61/1.62 tff(10046,plain,
% 1.61/1.62 ((~xuntil22(s45)) | until21(s46)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10045, 4059, 9440])).
% 1.61/1.62 tff(10047,plain,
% 1.61/1.62 (until21(s46)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10046, 10042])).
% 1.61/1.62 tff(10048,plain,
% 1.61/1.62 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s46) | (~node20(s46)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s46) | (~node20(s46)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10049,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s46) | (~node20(s46)))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10050,plain,
% 1.61/1.62 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s46) | (~node20(s46))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10049, 10048])).
% 1.61/1.62 tff(10051,plain,
% 1.61/1.62 (~node20(s46)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10050, 8579, 9036])).
% 1.61/1.62 tff(10052,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s46) | node20(s46) | (~until21(s46)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s46) | node20(s46) | (~until21(s46)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10053,plain,
% 1.61/1.62 ((node20(s46) | (~until21(s46)) | xuntil22(s46)) <=> (xuntil22(s46) | node20(s46) | (~until21(s46)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10054,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s46) | (~until21(s46)) | xuntil22(s46))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s46) | node20(s46) | (~until21(s46))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10053])).
% 1.61/1.62 tff(10055,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s46) | (~until21(s46)) | xuntil22(s46))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s46) | node20(s46) | (~until21(s46)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10054, 10052])).
% 1.61/1.62 tff(10056,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s46) | (~until21(s46)) | xuntil22(s46))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10057,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s46) | node20(s46) | (~until21(s46))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10056, 10055])).
% 1.61/1.62 tff(10058,plain,
% 1.61/1.62 (xuntil22(s46) | (~until21(s46))),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10057, 9422, 10051])).
% 1.61/1.62 tff(10059,plain,
% 1.61/1.62 (xuntil22(s46)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10058, 10047])).
% 1.61/1.62 tff(10060,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s46, s47)) | (~xuntil22(s46)) | until21(s47))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s46, s47)) | (~xuntil22(s46)) | until21(s47))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10061,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s46, s47)) | (~xuntil22(s46)) | until21(s47))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10062,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s46, s47)) | (~xuntil22(s46)) | until21(s47)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10061, 10060])).
% 1.61/1.62 tff(10063,plain,
% 1.61/1.62 ((~xuntil22(s46)) | until21(s47)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10062, 4123, 9440])).
% 1.61/1.62 tff(10064,plain,
% 1.61/1.62 (until21(s47)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10063, 10059])).
% 1.61/1.62 tff(10065,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s47) | node20(s47) | (~until21(s47)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s47) | node20(s47) | (~until21(s47)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10066,plain,
% 1.61/1.62 ((node20(s47) | (~until21(s47)) | xuntil22(s47)) <=> (xuntil22(s47) | node20(s47) | (~until21(s47)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10067,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s47) | (~until21(s47)) | xuntil22(s47))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s47) | node20(s47) | (~until21(s47))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10066])).
% 1.61/1.62 tff(10068,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s47) | (~until21(s47)) | xuntil22(s47))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s47) | node20(s47) | (~until21(s47)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10067, 10065])).
% 1.61/1.62 tff(10069,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s47) | (~until21(s47)) | xuntil22(s47))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10070,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s47) | node20(s47) | (~until21(s47))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10069, 10068])).
% 1.61/1.62 tff(10071,plain,
% 1.61/1.62 (xuntil22(s47)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10070, 9422, 10064, 9029])).
% 1.61/1.62 tff(10072,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s47, s48)) | (~xuntil22(s47)) | until21(s48))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s47, s48)) | (~xuntil22(s47)) | until21(s48))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10073,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s47, s48)) | (~xuntil22(s47)) | until21(s48))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10074,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s47, s48)) | (~xuntil22(s47)) | until21(s48)),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10073, 10072])).
% 1.61/1.62 tff(10075,plain,
% 1.61/1.62 ((~xuntil22(s47)) | until21(s48)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10074, 4198, 9440])).
% 1.61/1.62 tff(10076,plain,
% 1.61/1.62 (until21(s48)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10075, 10071])).
% 1.61/1.62 tff(10077,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s48) | node20(s48) | (~until21(s48)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s48) | node20(s48) | (~until21(s48)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10078,plain,
% 1.61/1.62 ((node20(s48) | (~until21(s48)) | xuntil22(s48)) <=> (xuntil22(s48) | node20(s48) | (~until21(s48)))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10079,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s48) | (~until21(s48)) | xuntil22(s48))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s48) | node20(s48) | (~until21(s48))))),
% 1.61/1.62 inference(monotonicity,[status(thm)],[10078])).
% 1.61/1.62 tff(10080,plain,
% 1.61/1.62 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s48) | (~until21(s48)) | xuntil22(s48))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s48) | node20(s48) | (~until21(s48)))),
% 1.61/1.62 inference(transitivity,[status(thm)],[10079, 10077])).
% 1.61/1.62 tff(10081,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s48) | (~until21(s48)) | xuntil22(s48))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10082,plain,
% 1.61/1.62 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s48) | node20(s48) | (~until21(s48))),
% 1.61/1.62 inference(modus_ponens,[status(thm)],[10081, 10080])).
% 1.61/1.62 tff(10083,plain,
% 1.61/1.62 (xuntil22(s48) | node20(s48)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10082, 9422, 10076])).
% 1.61/1.62 tff(10084,plain,
% 1.61/1.62 (xuntil22(s48)),
% 1.61/1.62 inference(unit_resolution,[status(thm)],[10083, 9021])).
% 1.61/1.62 tff(10085,plain,
% 1.61/1.62 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s48, s49)) | (~xuntil22(s48)) | until21(s49))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s48, s49)) | (~xuntil22(s48)) | until21(s49))),
% 1.61/1.62 inference(rewrite,[status(thm)],[])).
% 1.61/1.62 tff(10086,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s48, s49)) | (~xuntil22(s48)) | until21(s49))),
% 1.61/1.62 inference(quant_inst,[status(thm)],[])).
% 1.61/1.62 tff(10087,plain,
% 1.61/1.62 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s48, s49)) | (~xuntil22(s48)) | until21(s49)),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10086, 10085])).
% 1.61/1.63 tff(10088,plain,
% 1.61/1.63 ((~xuntil22(s48)) | until21(s49)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10087, 4287, 9440])).
% 1.61/1.63 tff(10089,plain,
% 1.61/1.63 (until21(s49)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10088, 10084])).
% 1.61/1.63 tff(10090,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s49) | node20(s49) | (~until21(s49)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s49) | node20(s49) | (~until21(s49)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10091,plain,
% 1.61/1.63 ((node20(s49) | (~until21(s49)) | xuntil22(s49)) <=> (xuntil22(s49) | node20(s49) | (~until21(s49)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10092,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s49) | (~until21(s49)) | xuntil22(s49))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s49) | node20(s49) | (~until21(s49))))),
% 1.61/1.63 inference(monotonicity,[status(thm)],[10091])).
% 1.61/1.63 tff(10093,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s49) | (~until21(s49)) | xuntil22(s49))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s49) | node20(s49) | (~until21(s49)))),
% 1.61/1.63 inference(transitivity,[status(thm)],[10092, 10090])).
% 1.61/1.63 tff(10094,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s49) | (~until21(s49)) | xuntil22(s49))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10095,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s49) | node20(s49) | (~until21(s49))),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10094, 10093])).
% 1.61/1.63 tff(10096,plain,
% 1.61/1.63 (xuntil22(s49)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10095, 9422, 10089, 9012])).
% 1.61/1.63 tff(10097,plain,
% 1.61/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s49, s50)) | (~xuntil22(s49)) | until21(s50))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s49, s50)) | (~xuntil22(s49)) | until21(s50))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10098,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s49, s50)) | (~xuntil22(s49)) | until21(s50))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10099,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s49, s50)) | (~xuntil22(s49)) | until21(s50)),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10098, 10097])).
% 1.61/1.63 tff(10100,plain,
% 1.61/1.63 ((~xuntil22(s49)) | until21(s50)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10099, 4354, 9440])).
% 1.61/1.63 tff(10101,plain,
% 1.61/1.63 (until21(s50)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10100, 10096])).
% 1.61/1.63 tff(10102,plain,
% 1.61/1.63 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s50) | (~node20(s50)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s50) | (~node20(s50)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10103,plain,
% 1.61/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s50) | (~node20(s50)))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10104,plain,
% 1.61/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s50) | (~node20(s50))),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10103, 10102])).
% 1.61/1.63 tff(10105,plain,
% 1.61/1.63 (~node20(s50)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10104, 8579, 9003])).
% 1.61/1.63 tff(10106,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s50) | node20(s50) | (~until21(s50)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s50) | node20(s50) | (~until21(s50)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10107,plain,
% 1.61/1.63 ((node20(s50) | (~until21(s50)) | xuntil22(s50)) <=> (xuntil22(s50) | node20(s50) | (~until21(s50)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10108,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s50) | (~until21(s50)) | xuntil22(s50))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s50) | node20(s50) | (~until21(s50))))),
% 1.61/1.63 inference(monotonicity,[status(thm)],[10107])).
% 1.61/1.63 tff(10109,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s50) | (~until21(s50)) | xuntil22(s50))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s50) | node20(s50) | (~until21(s50)))),
% 1.61/1.63 inference(transitivity,[status(thm)],[10108, 10106])).
% 1.61/1.63 tff(10110,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s50) | (~until21(s50)) | xuntil22(s50))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10111,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s50) | node20(s50) | (~until21(s50))),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10110, 10109])).
% 1.61/1.63 tff(10112,plain,
% 1.61/1.63 (xuntil22(s50) | (~until21(s50))),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10111, 9422, 10105])).
% 1.61/1.63 tff(10113,plain,
% 1.61/1.63 (xuntil22(s50)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10112, 10101])).
% 1.61/1.63 tff(10114,plain,
% 1.61/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s50, s51)) | (~xuntil22(s50)) | until21(s51))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s50, s51)) | (~xuntil22(s50)) | until21(s51))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10115,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s50, s51)) | (~xuntil22(s50)) | until21(s51))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10116,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s50, s51)) | (~xuntil22(s50)) | until21(s51)),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10115, 10114])).
% 1.61/1.63 tff(10117,plain,
% 1.61/1.63 ((~xuntil22(s50)) | until21(s51)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10116, 4453, 9440])).
% 1.61/1.63 tff(10118,plain,
% 1.61/1.63 (until21(s51)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10117, 10113])).
% 1.61/1.63 tff(10119,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s51) | node20(s51) | (~until21(s51)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s51) | node20(s51) | (~until21(s51)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10120,plain,
% 1.61/1.63 ((node20(s51) | (~until21(s51)) | xuntil22(s51)) <=> (xuntil22(s51) | node20(s51) | (~until21(s51)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10121,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s51) | (~until21(s51)) | xuntil22(s51))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s51) | node20(s51) | (~until21(s51))))),
% 1.61/1.63 inference(monotonicity,[status(thm)],[10120])).
% 1.61/1.63 tff(10122,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s51) | (~until21(s51)) | xuntil22(s51))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s51) | node20(s51) | (~until21(s51)))),
% 1.61/1.63 inference(transitivity,[status(thm)],[10121, 10119])).
% 1.61/1.63 tff(10123,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s51) | (~until21(s51)) | xuntil22(s51))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10124,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s51) | node20(s51) | (~until21(s51))),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10123, 10122])).
% 1.61/1.63 tff(10125,plain,
% 1.61/1.63 (xuntil22(s51)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10124, 9422, 10118, 8996])).
% 1.61/1.63 tff(10126,plain,
% 1.61/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s51, s52)) | (~xuntil22(s51)) | until21(s52))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s51, s52)) | (~xuntil22(s51)) | until21(s52))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10127,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s51, s52)) | (~xuntil22(s51)) | until21(s52))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10128,plain,
% 1.61/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s51, s52)) | (~xuntil22(s51)) | until21(s52)),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10127, 10126])).
% 1.61/1.63 tff(10129,plain,
% 1.61/1.63 ((~xuntil22(s51)) | until21(s52)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10128, 4531, 9440])).
% 1.61/1.63 tff(10130,plain,
% 1.61/1.63 (until21(s52)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10129, 10125])).
% 1.61/1.63 tff(10131,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s52) | node20(s52) | (~until21(s52)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s52) | node20(s52) | (~until21(s52)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10132,plain,
% 1.61/1.63 ((node20(s52) | (~until21(s52)) | xuntil22(s52)) <=> (xuntil22(s52) | node20(s52) | (~until21(s52)))),
% 1.61/1.63 inference(rewrite,[status(thm)],[])).
% 1.61/1.63 tff(10133,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s52) | (~until21(s52)) | xuntil22(s52))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s52) | node20(s52) | (~until21(s52))))),
% 1.61/1.63 inference(monotonicity,[status(thm)],[10132])).
% 1.61/1.63 tff(10134,plain,
% 1.61/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s52) | (~until21(s52)) | xuntil22(s52))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s52) | node20(s52) | (~until21(s52)))),
% 1.61/1.63 inference(transitivity,[status(thm)],[10133, 10131])).
% 1.61/1.63 tff(10135,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s52) | (~until21(s52)) | xuntil22(s52))),
% 1.61/1.63 inference(quant_inst,[status(thm)],[])).
% 1.61/1.63 tff(10136,plain,
% 1.61/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s52) | node20(s52) | (~until21(s52))),
% 1.61/1.63 inference(modus_ponens,[status(thm)],[10135, 10134])).
% 1.61/1.63 tff(10137,plain,
% 1.61/1.63 (xuntil22(s52) | node20(s52)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10136, 9422, 10130])).
% 1.61/1.63 tff(10138,plain,
% 1.61/1.63 (xuntil22(s52)),
% 1.61/1.63 inference(unit_resolution,[status(thm)],[10137, 8988])).
% 1.61/1.63 tff(10139,plain,
% 1.61/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s52, s53)) | (~xuntil22(s52)) | until21(s53))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s52, s53)) | (~xuntil22(s52)) | until21(s53))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10140,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s52, s53)) | (~xuntil22(s52)) | until21(s53))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10141,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s52, s53)) | (~xuntil22(s52)) | until21(s53)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10140, 10139])).
% 1.71/1.63 tff(10142,plain,
% 1.71/1.63 ((~xuntil22(s52)) | until21(s53)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10141, 4592, 9440])).
% 1.71/1.63 tff(10143,plain,
% 1.71/1.63 (until21(s53)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10142, 10138])).
% 1.71/1.63 tff(10144,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s53) | node20(s53) | (~until21(s53)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s53) | node20(s53) | (~until21(s53)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10145,plain,
% 1.71/1.63 ((node20(s53) | (~until21(s53)) | xuntil22(s53)) <=> (xuntil22(s53) | node20(s53) | (~until21(s53)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10146,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s53) | (~until21(s53)) | xuntil22(s53))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s53) | node20(s53) | (~until21(s53))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10145])).
% 1.71/1.63 tff(10147,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s53) | (~until21(s53)) | xuntil22(s53))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s53) | node20(s53) | (~until21(s53)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10146, 10144])).
% 1.71/1.63 tff(10148,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s53) | (~until21(s53)) | xuntil22(s53))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10149,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s53) | node20(s53) | (~until21(s53))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10148, 10147])).
% 1.71/1.63 tff(10150,plain,
% 1.71/1.63 (xuntil22(s53)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10149, 9422, 10143, 8979])).
% 1.71/1.63 tff(10151,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s53, s54)) | (~xuntil22(s53)) | until21(s54))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s53, s54)) | (~xuntil22(s53)) | until21(s54))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10152,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s53, s54)) | (~xuntil22(s53)) | until21(s54))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10153,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s53, s54)) | (~xuntil22(s53)) | until21(s54)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10152, 10151])).
% 1.71/1.63 tff(10154,plain,
% 1.71/1.63 ((~xuntil22(s53)) | until21(s54)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10153, 4687, 9440])).
% 1.71/1.63 tff(10155,plain,
% 1.71/1.63 (until21(s54)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10154, 10150])).
% 1.71/1.63 tff(10156,plain,
% 1.71/1.63 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s54) | (~node20(s54)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s54) | (~node20(s54)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10157,plain,
% 1.71/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s54) | (~node20(s54)))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10158,plain,
% 1.71/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s54) | (~node20(s54))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10157, 10156])).
% 1.71/1.63 tff(10159,plain,
% 1.71/1.63 (~node20(s54)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10158, 8579, 8970])).
% 1.71/1.63 tff(10160,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s54) | node20(s54) | (~until21(s54)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s54) | node20(s54) | (~until21(s54)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10161,plain,
% 1.71/1.63 ((node20(s54) | (~until21(s54)) | xuntil22(s54)) <=> (xuntil22(s54) | node20(s54) | (~until21(s54)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10162,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s54) | (~until21(s54)) | xuntil22(s54))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s54) | node20(s54) | (~until21(s54))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10161])).
% 1.71/1.63 tff(10163,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s54) | (~until21(s54)) | xuntil22(s54))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s54) | node20(s54) | (~until21(s54)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10162, 10160])).
% 1.71/1.63 tff(10164,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s54) | (~until21(s54)) | xuntil22(s54))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10165,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s54) | node20(s54) | (~until21(s54))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10164, 10163])).
% 1.71/1.63 tff(10166,plain,
% 1.71/1.63 (xuntil22(s54) | (~until21(s54))),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10165, 9422, 10159])).
% 1.71/1.63 tff(10167,plain,
% 1.71/1.63 (xuntil22(s54)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10166, 10155])).
% 1.71/1.63 tff(10168,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s54, s55)) | (~xuntil22(s54)) | until21(s55))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s54, s55)) | (~xuntil22(s54)) | until21(s55))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10169,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s54, s55)) | (~xuntil22(s54)) | until21(s55))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10170,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s54, s55)) | (~xuntil22(s54)) | until21(s55)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10169, 10168])).
% 1.71/1.63 tff(10171,plain,
% 1.71/1.63 ((~xuntil22(s54)) | until21(s55)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10170, 4751, 9440])).
% 1.71/1.63 tff(10172,plain,
% 1.71/1.63 (until21(s55)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10171, 10167])).
% 1.71/1.63 tff(10173,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s55) | node20(s55) | (~until21(s55)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s55) | node20(s55) | (~until21(s55)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10174,plain,
% 1.71/1.63 ((node20(s55) | (~until21(s55)) | xuntil22(s55)) <=> (xuntil22(s55) | node20(s55) | (~until21(s55)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10175,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s55) | (~until21(s55)) | xuntil22(s55))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s55) | node20(s55) | (~until21(s55))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10174])).
% 1.71/1.63 tff(10176,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s55) | (~until21(s55)) | xuntil22(s55))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s55) | node20(s55) | (~until21(s55)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10175, 10173])).
% 1.71/1.63 tff(10177,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s55) | (~until21(s55)) | xuntil22(s55))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10178,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s55) | node20(s55) | (~until21(s55))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10177, 10176])).
% 1.71/1.63 tff(10179,plain,
% 1.71/1.63 (xuntil22(s55)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10178, 9422, 10172, 8963])).
% 1.71/1.63 tff(10180,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s55, s56)) | (~xuntil22(s55)) | until21(s56))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s55, s56)) | (~xuntil22(s55)) | until21(s56))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10181,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s55, s56)) | (~xuntil22(s55)) | until21(s56))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10182,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s55, s56)) | (~xuntil22(s55)) | until21(s56)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10181, 10180])).
% 1.71/1.63 tff(10183,plain,
% 1.71/1.63 ((~xuntil22(s55)) | until21(s56)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10182, 4826, 9440])).
% 1.71/1.63 tff(10184,plain,
% 1.71/1.63 (until21(s56)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10183, 10179])).
% 1.71/1.63 tff(10185,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s56) | node20(s56) | (~until21(s56)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s56) | node20(s56) | (~until21(s56)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10186,plain,
% 1.71/1.63 ((node20(s56) | (~until21(s56)) | xuntil22(s56)) <=> (xuntil22(s56) | node20(s56) | (~until21(s56)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10187,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s56) | (~until21(s56)) | xuntil22(s56))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s56) | node20(s56) | (~until21(s56))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10186])).
% 1.71/1.63 tff(10188,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s56) | (~until21(s56)) | xuntil22(s56))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s56) | node20(s56) | (~until21(s56)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10187, 10185])).
% 1.71/1.63 tff(10189,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s56) | (~until21(s56)) | xuntil22(s56))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10190,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s56) | node20(s56) | (~until21(s56))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10189, 10188])).
% 1.71/1.63 tff(10191,plain,
% 1.71/1.63 (xuntil22(s56) | node20(s56)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10190, 9422, 10184])).
% 1.71/1.63 tff(10192,plain,
% 1.71/1.63 (xuntil22(s56)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10191, 8955])).
% 1.71/1.63 tff(10193,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s56, s57)) | (~xuntil22(s56)) | until21(s57))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s56, s57)) | (~xuntil22(s56)) | until21(s57))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10194,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s56, s57)) | (~xuntil22(s56)) | until21(s57))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10195,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s56, s57)) | (~xuntil22(s56)) | until21(s57)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 1.71/1.63 tff(10196,plain,
% 1.71/1.63 ((~xuntil22(s56)) | until21(s57)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10195, 4915, 9440])).
% 1.71/1.63 tff(10197,plain,
% 1.71/1.63 (until21(s57)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10196, 10192])).
% 1.71/1.63 tff(10198,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s57) | node20(s57) | (~until21(s57)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s57) | node20(s57) | (~until21(s57)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10199,plain,
% 1.71/1.63 ((node20(s57) | (~until21(s57)) | xuntil22(s57)) <=> (xuntil22(s57) | node20(s57) | (~until21(s57)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10200,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s57) | (~until21(s57)) | xuntil22(s57))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s57) | node20(s57) | (~until21(s57))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10199])).
% 1.71/1.63 tff(10201,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s57) | (~until21(s57)) | xuntil22(s57))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s57) | node20(s57) | (~until21(s57)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10200, 10198])).
% 1.71/1.63 tff(10202,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s57) | (~until21(s57)) | xuntil22(s57))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10203,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s57) | node20(s57) | (~until21(s57))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10202, 10201])).
% 1.71/1.63 tff(10204,plain,
% 1.71/1.63 (xuntil22(s57)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10203, 9422, 10197, 8946])).
% 1.71/1.63 tff(10205,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s57, s58)) | (~xuntil22(s57)) | until21(s58))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s57, s58)) | (~xuntil22(s57)) | until21(s58))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10206,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s57, s58)) | (~xuntil22(s57)) | until21(s58))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10207,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s57, s58)) | (~xuntil22(s57)) | until21(s58)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10206, 10205])).
% 1.71/1.63 tff(10208,plain,
% 1.71/1.63 ((~xuntil22(s57)) | until21(s58)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10207, 4982, 9440])).
% 1.71/1.63 tff(10209,plain,
% 1.71/1.63 (until21(s58)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10208, 10204])).
% 1.71/1.63 tff(10210,plain,
% 1.71/1.63 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s58) | (~node20(s58)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s58) | (~node20(s58)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10211,plain,
% 1.71/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s58) | (~node20(s58)))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10212,plain,
% 1.71/1.63 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s58) | (~node20(s58))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10211, 10210])).
% 1.71/1.63 tff(10213,plain,
% 1.71/1.63 (~node20(s58)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10212, 8579, 8937])).
% 1.71/1.63 tff(10214,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s58) | node20(s58) | (~until21(s58)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s58) | node20(s58) | (~until21(s58)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10215,plain,
% 1.71/1.63 ((node20(s58) | (~until21(s58)) | xuntil22(s58)) <=> (xuntil22(s58) | node20(s58) | (~until21(s58)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10216,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s58) | (~until21(s58)) | xuntil22(s58))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s58) | node20(s58) | (~until21(s58))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10215])).
% 1.71/1.63 tff(10217,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s58) | (~until21(s58)) | xuntil22(s58))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s58) | node20(s58) | (~until21(s58)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10216, 10214])).
% 1.71/1.63 tff(10218,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s58) | (~until21(s58)) | xuntil22(s58))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10219,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s58) | node20(s58) | (~until21(s58))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10218, 10217])).
% 1.71/1.63 tff(10220,plain,
% 1.71/1.63 (xuntil22(s58) | (~until21(s58))),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10219, 9422, 10213])).
% 1.71/1.63 tff(10221,plain,
% 1.71/1.63 (xuntil22(s58)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10220, 10209])).
% 1.71/1.63 tff(10222,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s58, s59)) | (~xuntil22(s58)) | until21(s59))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s58, s59)) | (~xuntil22(s58)) | until21(s59))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10223,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s58, s59)) | (~xuntil22(s58)) | until21(s59))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10224,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s58, s59)) | (~xuntil22(s58)) | until21(s59)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10223, 10222])).
% 1.71/1.63 tff(10225,plain,
% 1.71/1.63 ((~xuntil22(s58)) | until21(s59)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10224, 5081, 9440])).
% 1.71/1.63 tff(10226,plain,
% 1.71/1.63 (until21(s59)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10225, 10221])).
% 1.71/1.63 tff(10227,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s59) | node20(s59) | (~until21(s59)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s59) | node20(s59) | (~until21(s59)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10228,plain,
% 1.71/1.63 ((node20(s59) | (~until21(s59)) | xuntil22(s59)) <=> (xuntil22(s59) | node20(s59) | (~until21(s59)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10229,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s59) | (~until21(s59)) | xuntil22(s59))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s59) | node20(s59) | (~until21(s59))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10228])).
% 1.71/1.63 tff(10230,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s59) | (~until21(s59)) | xuntil22(s59))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s59) | node20(s59) | (~until21(s59)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10229, 10227])).
% 1.71/1.63 tff(10231,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s59) | (~until21(s59)) | xuntil22(s59))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10232,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s59) | node20(s59) | (~until21(s59))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10231, 10230])).
% 1.71/1.63 tff(10233,plain,
% 1.71/1.63 (xuntil22(s59)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10232, 9422, 10226, 8930])).
% 1.71/1.63 tff(10234,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s59, s60)) | (~xuntil22(s59)) | until21(s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s59, s60)) | (~xuntil22(s59)) | until21(s60))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10235,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s59, s60)) | (~xuntil22(s59)) | until21(s60))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10236,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s59, s60)) | (~xuntil22(s59)) | until21(s60)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10235, 10234])).
% 1.71/1.63 tff(10237,plain,
% 1.71/1.63 ((~xuntil22(s59)) | until21(s60)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10236, 5159, 9440])).
% 1.71/1.63 tff(10238,plain,
% 1.71/1.63 (until21(s60)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10237, 10233])).
% 1.71/1.63 tff(10239,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s60) | node20(s60) | (~until21(s60)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s60) | node20(s60) | (~until21(s60)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10240,plain,
% 1.71/1.63 ((node20(s60) | (~until21(s60)) | xuntil22(s60)) <=> (xuntil22(s60) | node20(s60) | (~until21(s60)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10241,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s60) | (~until21(s60)) | xuntil22(s60))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s60) | node20(s60) | (~until21(s60))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10240])).
% 1.71/1.63 tff(10242,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s60) | (~until21(s60)) | xuntil22(s60))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s60) | node20(s60) | (~until21(s60)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10241, 10239])).
% 1.71/1.63 tff(10243,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s60) | (~until21(s60)) | xuntil22(s60))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10244,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s60) | node20(s60) | (~until21(s60))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10243, 10242])).
% 1.71/1.63 tff(10245,plain,
% 1.71/1.63 (xuntil22(s60) | node20(s60)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10244, 9422, 10238])).
% 1.71/1.63 tff(10246,plain,
% 1.71/1.63 (xuntil22(s60)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10245, 8922])).
% 1.71/1.63 tff(10247,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s60, s61)) | (~xuntil22(s60)) | until21(s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s60, s61)) | (~xuntil22(s60)) | until21(s61))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10248,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s60, s61)) | (~xuntil22(s60)) | until21(s61))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10249,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s60, s61)) | (~xuntil22(s60)) | until21(s61)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10248, 10247])).
% 1.71/1.63 tff(10250,plain,
% 1.71/1.63 ((~xuntil22(s60)) | until21(s61)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10249, 5220, 9440])).
% 1.71/1.63 tff(10251,plain,
% 1.71/1.63 (until21(s61)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10250, 10246])).
% 1.71/1.63 tff(10252,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s61) | node20(s61) | (~until21(s61)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s61) | node20(s61) | (~until21(s61)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10253,plain,
% 1.71/1.63 ((node20(s61) | (~until21(s61)) | xuntil22(s61)) <=> (xuntil22(s61) | node20(s61) | (~until21(s61)))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10254,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s61) | (~until21(s61)) | xuntil22(s61))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s61) | node20(s61) | (~until21(s61))))),
% 1.71/1.63 inference(monotonicity,[status(thm)],[10253])).
% 1.71/1.63 tff(10255,plain,
% 1.71/1.63 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s61) | (~until21(s61)) | xuntil22(s61))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s61) | node20(s61) | (~until21(s61)))),
% 1.71/1.63 inference(transitivity,[status(thm)],[10254, 10252])).
% 1.71/1.63 tff(10256,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s61) | (~until21(s61)) | xuntil22(s61))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10257,plain,
% 1.71/1.63 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s61) | node20(s61) | (~until21(s61))),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10256, 10255])).
% 1.71/1.63 tff(10258,plain,
% 1.71/1.63 (xuntil22(s61)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10257, 9422, 10251, 8913])).
% 1.71/1.63 tff(10259,plain,
% 1.71/1.63 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s61, s62)) | (~xuntil22(s61)) | until21(s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s61, s62)) | (~xuntil22(s61)) | until21(s62))),
% 1.71/1.63 inference(rewrite,[status(thm)],[])).
% 1.71/1.63 tff(10260,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s61, s62)) | (~xuntil22(s61)) | until21(s62))),
% 1.71/1.63 inference(quant_inst,[status(thm)],[])).
% 1.71/1.63 tff(10261,plain,
% 1.71/1.63 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s61, s62)) | (~xuntil22(s61)) | until21(s62)),
% 1.71/1.63 inference(modus_ponens,[status(thm)],[10260, 10259])).
% 1.71/1.63 tff(10262,plain,
% 1.71/1.63 ((~xuntil22(s61)) | until21(s62)),
% 1.71/1.63 inference(unit_resolution,[status(thm)],[10261, 5315, 9440])).
% 1.71/1.63 tff(10263,plain,
% 1.71/1.64 (until21(s62)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10262, 10258])).
% 1.71/1.64 tff(10264,plain,
% 1.71/1.64 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s62) | (~node20(s62)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s62) | (~node20(s62)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10265,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s62) | (~node20(s62)))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10266,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s62) | (~node20(s62))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10265, 10264])).
% 1.71/1.64 tff(10267,plain,
% 1.71/1.64 (~node20(s62)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10266, 8579, 8904])).
% 1.71/1.64 tff(10268,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s62) | node20(s62) | (~until21(s62)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s62) | node20(s62) | (~until21(s62)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10269,plain,
% 1.71/1.64 ((node20(s62) | (~until21(s62)) | xuntil22(s62)) <=> (xuntil22(s62) | node20(s62) | (~until21(s62)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10270,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s62) | (~until21(s62)) | xuntil22(s62))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s62) | node20(s62) | (~until21(s62))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10269])).
% 1.71/1.64 tff(10271,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s62) | (~until21(s62)) | xuntil22(s62))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s62) | node20(s62) | (~until21(s62)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10270, 10268])).
% 1.71/1.64 tff(10272,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s62) | (~until21(s62)) | xuntil22(s62))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10273,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s62) | node20(s62) | (~until21(s62))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10272, 10271])).
% 1.71/1.64 tff(10274,plain,
% 1.71/1.64 (xuntil22(s62) | (~until21(s62))),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10273, 9422, 10267])).
% 1.71/1.64 tff(10275,plain,
% 1.71/1.64 (xuntil22(s62)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10274, 10263])).
% 1.71/1.64 tff(10276,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s62, s63)) | (~xuntil22(s62)) | until21(s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s62, s63)) | (~xuntil22(s62)) | until21(s63))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10277,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s62, s63)) | (~xuntil22(s62)) | until21(s63))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10278,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s62, s63)) | (~xuntil22(s62)) | until21(s63)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10277, 10276])).
% 1.71/1.64 tff(10279,plain,
% 1.71/1.64 ((~xuntil22(s62)) | until21(s63)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10278, 5379, 9440])).
% 1.71/1.64 tff(10280,plain,
% 1.71/1.64 (until21(s63)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10279, 10275])).
% 1.71/1.64 tff(10281,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s63) | node20(s63) | (~until21(s63)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s63) | node20(s63) | (~until21(s63)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10282,plain,
% 1.71/1.64 ((node20(s63) | (~until21(s63)) | xuntil22(s63)) <=> (xuntil22(s63) | node20(s63) | (~until21(s63)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10283,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s63) | (~until21(s63)) | xuntil22(s63))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s63) | node20(s63) | (~until21(s63))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10282])).
% 1.71/1.64 tff(10284,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s63) | (~until21(s63)) | xuntil22(s63))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s63) | node20(s63) | (~until21(s63)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10283, 10281])).
% 1.71/1.64 tff(10285,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s63) | (~until21(s63)) | xuntil22(s63))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10286,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s63) | node20(s63) | (~until21(s63))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10285, 10284])).
% 1.71/1.64 tff(10287,plain,
% 1.71/1.64 (xuntil22(s63)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10286, 9422, 10280, 8897])).
% 1.71/1.64 tff(10288,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s63, s64)) | (~xuntil22(s63)) | until21(s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s63, s64)) | (~xuntil22(s63)) | until21(s64))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10289,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s63, s64)) | (~xuntil22(s63)) | until21(s64))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10290,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s63, s64)) | (~xuntil22(s63)) | until21(s64)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10289, 10288])).
% 1.71/1.64 tff(10291,plain,
% 1.71/1.64 ((~xuntil22(s63)) | until21(s64)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10290, 5454, 9440])).
% 1.71/1.64 tff(10292,plain,
% 1.71/1.64 (until21(s64)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10291, 10287])).
% 1.71/1.64 tff(10293,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s64) | node20(s64) | (~until21(s64)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s64) | node20(s64) | (~until21(s64)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10294,plain,
% 1.71/1.64 ((node20(s64) | (~until21(s64)) | xuntil22(s64)) <=> (xuntil22(s64) | node20(s64) | (~until21(s64)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10295,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s64) | (~until21(s64)) | xuntil22(s64))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s64) | node20(s64) | (~until21(s64))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10294])).
% 1.71/1.64 tff(10296,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s64) | (~until21(s64)) | xuntil22(s64))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s64) | node20(s64) | (~until21(s64)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10295, 10293])).
% 1.71/1.64 tff(10297,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s64) | (~until21(s64)) | xuntil22(s64))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10298,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s64) | node20(s64) | (~until21(s64))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10297, 10296])).
% 1.71/1.64 tff(10299,plain,
% 1.71/1.64 (xuntil22(s64) | node20(s64)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10298, 9422, 10292])).
% 1.71/1.64 tff(10300,plain,
% 1.71/1.64 (xuntil22(s64)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10299, 8889])).
% 1.71/1.64 tff(10301,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s64, s65)) | (~xuntil22(s64)) | until21(s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s64, s65)) | (~xuntil22(s64)) | until21(s65))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10302,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s64, s65)) | (~xuntil22(s64)) | until21(s65))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10303,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s64, s65)) | (~xuntil22(s64)) | until21(s65)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10302, 10301])).
% 1.71/1.64 tff(10304,plain,
% 1.71/1.64 ((~xuntil22(s64)) | until21(s65)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10303, 5543, 9440])).
% 1.71/1.64 tff(10305,plain,
% 1.71/1.64 (until21(s65)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10304, 10300])).
% 1.71/1.64 tff(10306,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s65) | node20(s65) | (~until21(s65)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s65) | node20(s65) | (~until21(s65)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10307,plain,
% 1.71/1.64 ((node20(s65) | (~until21(s65)) | xuntil22(s65)) <=> (xuntil22(s65) | node20(s65) | (~until21(s65)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10308,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s65) | (~until21(s65)) | xuntil22(s65))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s65) | node20(s65) | (~until21(s65))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10307])).
% 1.71/1.64 tff(10309,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s65) | (~until21(s65)) | xuntil22(s65))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s65) | node20(s65) | (~until21(s65)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10308, 10306])).
% 1.71/1.64 tff(10310,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s65) | (~until21(s65)) | xuntil22(s65))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10311,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s65) | node20(s65) | (~until21(s65))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10310, 10309])).
% 1.71/1.64 tff(10312,plain,
% 1.71/1.64 (xuntil22(s65)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10311, 9422, 10305, 8880])).
% 1.71/1.64 tff(10313,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s65, s66)) | (~xuntil22(s65)) | until21(s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s65, s66)) | (~xuntil22(s65)) | until21(s66))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10314,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s65, s66)) | (~xuntil22(s65)) | until21(s66))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10315,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s65, s66)) | (~xuntil22(s65)) | until21(s66)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10314, 10313])).
% 1.71/1.64 tff(10316,plain,
% 1.71/1.64 ((~xuntil22(s65)) | until21(s66)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10315, 5610, 9440])).
% 1.71/1.64 tff(10317,plain,
% 1.71/1.64 (until21(s66)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10316, 10312])).
% 1.71/1.64 tff(10318,plain,
% 1.71/1.64 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s66) | (~node20(s66)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s66) | (~node20(s66)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10319,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s66) | (~node20(s66)))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10320,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s66) | (~node20(s66))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10319, 10318])).
% 1.71/1.64 tff(10321,plain,
% 1.71/1.64 (~node20(s66)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10320, 8579, 8871])).
% 1.71/1.64 tff(10322,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s66) | node20(s66) | (~until21(s66)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s66) | node20(s66) | (~until21(s66)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10323,plain,
% 1.71/1.64 ((node20(s66) | (~until21(s66)) | xuntil22(s66)) <=> (xuntil22(s66) | node20(s66) | (~until21(s66)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10324,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s66) | (~until21(s66)) | xuntil22(s66))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s66) | node20(s66) | (~until21(s66))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10323])).
% 1.71/1.64 tff(10325,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s66) | (~until21(s66)) | xuntil22(s66))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s66) | node20(s66) | (~until21(s66)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10324, 10322])).
% 1.71/1.64 tff(10326,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s66) | (~until21(s66)) | xuntil22(s66))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10327,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s66) | node20(s66) | (~until21(s66))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10326, 10325])).
% 1.71/1.64 tff(10328,plain,
% 1.71/1.64 (xuntil22(s66) | (~until21(s66))),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10327, 9422, 10321])).
% 1.71/1.64 tff(10329,plain,
% 1.71/1.64 (xuntil22(s66)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10328, 10317])).
% 1.71/1.64 tff(10330,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s66, s67)) | (~xuntil22(s66)) | until21(s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s66, s67)) | (~xuntil22(s66)) | until21(s67))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10331,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s66, s67)) | (~xuntil22(s66)) | until21(s67))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10332,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s66, s67)) | (~xuntil22(s66)) | until21(s67)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10331, 10330])).
% 1.71/1.64 tff(10333,plain,
% 1.71/1.64 ((~xuntil22(s66)) | until21(s67)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10332, 5709, 9440])).
% 1.71/1.64 tff(10334,plain,
% 1.71/1.64 (until21(s67)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10333, 10329])).
% 1.71/1.64 tff(10335,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s67) | node20(s67) | (~until21(s67)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s67) | node20(s67) | (~until21(s67)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10336,plain,
% 1.71/1.64 ((node20(s67) | (~until21(s67)) | xuntil22(s67)) <=> (xuntil22(s67) | node20(s67) | (~until21(s67)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10337,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s67) | (~until21(s67)) | xuntil22(s67))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s67) | node20(s67) | (~until21(s67))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10336])).
% 1.71/1.64 tff(10338,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s67) | (~until21(s67)) | xuntil22(s67))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s67) | node20(s67) | (~until21(s67)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10337, 10335])).
% 1.71/1.64 tff(10339,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s67) | (~until21(s67)) | xuntil22(s67))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10340,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s67) | node20(s67) | (~until21(s67))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10339, 10338])).
% 1.71/1.64 tff(10341,plain,
% 1.71/1.64 (xuntil22(s67)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10340, 9422, 10334, 8864])).
% 1.71/1.64 tff(10342,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s67, s68)) | (~xuntil22(s67)) | until21(s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s67, s68)) | (~xuntil22(s67)) | until21(s68))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10343,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s67, s68)) | (~xuntil22(s67)) | until21(s68))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10344,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s67, s68)) | (~xuntil22(s67)) | until21(s68)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10343, 10342])).
% 1.71/1.64 tff(10345,plain,
% 1.71/1.64 ((~xuntil22(s67)) | until21(s68)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10344, 5787, 9440])).
% 1.71/1.64 tff(10346,plain,
% 1.71/1.64 (until21(s68)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10345, 10341])).
% 1.71/1.64 tff(10347,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s68) | node20(s68) | (~until21(s68)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s68) | node20(s68) | (~until21(s68)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10348,plain,
% 1.71/1.64 ((node20(s68) | (~until21(s68)) | xuntil22(s68)) <=> (xuntil22(s68) | node20(s68) | (~until21(s68)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10349,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s68) | (~until21(s68)) | xuntil22(s68))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s68) | node20(s68) | (~until21(s68))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10348])).
% 1.71/1.64 tff(10350,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s68) | (~until21(s68)) | xuntil22(s68))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s68) | node20(s68) | (~until21(s68)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10349, 10347])).
% 1.71/1.64 tff(10351,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s68) | (~until21(s68)) | xuntil22(s68))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10352,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s68) | node20(s68) | (~until21(s68))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10351, 10350])).
% 1.71/1.64 tff(10353,plain,
% 1.71/1.64 (xuntil22(s68) | node20(s68)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10352, 9422, 10346])).
% 1.71/1.64 tff(10354,plain,
% 1.71/1.64 (xuntil22(s68)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10353, 8856])).
% 1.71/1.64 tff(10355,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s68, s69)) | (~xuntil22(s68)) | until21(s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s68, s69)) | (~xuntil22(s68)) | until21(s69))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10356,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s68, s69)) | (~xuntil22(s68)) | until21(s69))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10357,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s68, s69)) | (~xuntil22(s68)) | until21(s69)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10356, 10355])).
% 1.71/1.64 tff(10358,plain,
% 1.71/1.64 ((~xuntil22(s68)) | until21(s69)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10357, 5848, 9440])).
% 1.71/1.64 tff(10359,plain,
% 1.71/1.64 (until21(s69)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10358, 10354])).
% 1.71/1.64 tff(10360,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s69) | node20(s69) | (~until21(s69)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s69) | node20(s69) | (~until21(s69)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10361,plain,
% 1.71/1.64 ((node20(s69) | (~until21(s69)) | xuntil22(s69)) <=> (xuntil22(s69) | node20(s69) | (~until21(s69)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10362,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s69) | (~until21(s69)) | xuntil22(s69))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s69) | node20(s69) | (~until21(s69))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10361])).
% 1.71/1.64 tff(10363,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s69) | (~until21(s69)) | xuntil22(s69))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s69) | node20(s69) | (~until21(s69)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10362, 10360])).
% 1.71/1.64 tff(10364,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s69) | (~until21(s69)) | xuntil22(s69))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10365,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s69) | node20(s69) | (~until21(s69))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10364, 10363])).
% 1.71/1.64 tff(10366,plain,
% 1.71/1.64 (xuntil22(s69)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10365, 9422, 10359, 8847])).
% 1.71/1.64 tff(10367,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s69, s70)) | (~xuntil22(s69)) | until21(s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s69, s70)) | (~xuntil22(s69)) | until21(s70))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10368,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s69, s70)) | (~xuntil22(s69)) | until21(s70))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10369,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s69, s70)) | (~xuntil22(s69)) | until21(s70)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10368, 10367])).
% 1.71/1.64 tff(10370,plain,
% 1.71/1.64 ((~xuntil22(s69)) | until21(s70)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10369, 5943, 9440])).
% 1.71/1.64 tff(10371,plain,
% 1.71/1.64 (until21(s70)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10370, 10366])).
% 1.71/1.64 tff(10372,plain,
% 1.71/1.64 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s70) | (~node20(s70)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s70) | (~node20(s70)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10373,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s70) | (~node20(s70)))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10374,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s70) | (~node20(s70))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10373, 10372])).
% 1.71/1.64 tff(10375,plain,
% 1.71/1.64 (~node20(s70)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10374, 8579, 8838])).
% 1.71/1.64 tff(10376,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s70) | node20(s70) | (~until21(s70)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s70) | node20(s70) | (~until21(s70)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10377,plain,
% 1.71/1.64 ((node20(s70) | (~until21(s70)) | xuntil22(s70)) <=> (xuntil22(s70) | node20(s70) | (~until21(s70)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10378,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s70) | (~until21(s70)) | xuntil22(s70))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s70) | node20(s70) | (~until21(s70))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10377])).
% 1.71/1.64 tff(10379,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s70) | (~until21(s70)) | xuntil22(s70))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s70) | node20(s70) | (~until21(s70)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10378, 10376])).
% 1.71/1.64 tff(10380,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s70) | (~until21(s70)) | xuntil22(s70))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10381,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s70) | node20(s70) | (~until21(s70))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10380, 10379])).
% 1.71/1.64 tff(10382,plain,
% 1.71/1.64 (xuntil22(s70) | (~until21(s70))),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10381, 9422, 10375])).
% 1.71/1.64 tff(10383,plain,
% 1.71/1.64 (xuntil22(s70)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10382, 10371])).
% 1.71/1.64 tff(10384,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s70, s71)) | (~xuntil22(s70)) | until21(s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s70, s71)) | (~xuntil22(s70)) | until21(s71))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10385,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s70, s71)) | (~xuntil22(s70)) | until21(s71))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10386,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s70, s71)) | (~xuntil22(s70)) | until21(s71)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10385, 10384])).
% 1.71/1.64 tff(10387,plain,
% 1.71/1.64 ((~xuntil22(s70)) | until21(s71)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10386, 6007, 9440])).
% 1.71/1.64 tff(10388,plain,
% 1.71/1.64 (until21(s71)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10387, 10383])).
% 1.71/1.64 tff(10389,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s71) | node20(s71) | (~until21(s71)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s71) | node20(s71) | (~until21(s71)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10390,plain,
% 1.71/1.64 ((node20(s71) | (~until21(s71)) | xuntil22(s71)) <=> (xuntil22(s71) | node20(s71) | (~until21(s71)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10391,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s71) | (~until21(s71)) | xuntil22(s71))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s71) | node20(s71) | (~until21(s71))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10390])).
% 1.71/1.64 tff(10392,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s71) | (~until21(s71)) | xuntil22(s71))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s71) | node20(s71) | (~until21(s71)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10391, 10389])).
% 1.71/1.64 tff(10393,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s71) | (~until21(s71)) | xuntil22(s71))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10394,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s71) | node20(s71) | (~until21(s71))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10393, 10392])).
% 1.71/1.64 tff(10395,plain,
% 1.71/1.64 (xuntil22(s71)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10394, 9422, 10388, 8831])).
% 1.71/1.64 tff(10396,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s71, s72)) | (~xuntil22(s71)) | until21(s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s71, s72)) | (~xuntil22(s71)) | until21(s72))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10397,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s71, s72)) | (~xuntil22(s71)) | until21(s72))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10398,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s71, s72)) | (~xuntil22(s71)) | until21(s72)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10397, 10396])).
% 1.71/1.64 tff(10399,plain,
% 1.71/1.64 ((~xuntil22(s71)) | until21(s72)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10398, 6082, 9440])).
% 1.71/1.64 tff(10400,plain,
% 1.71/1.64 (until21(s72)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10399, 10395])).
% 1.71/1.64 tff(10401,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s72) | node20(s72) | (~until21(s72)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s72) | node20(s72) | (~until21(s72)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10402,plain,
% 1.71/1.64 ((node20(s72) | (~until21(s72)) | xuntil22(s72)) <=> (xuntil22(s72) | node20(s72) | (~until21(s72)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10403,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s72) | (~until21(s72)) | xuntil22(s72))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s72) | node20(s72) | (~until21(s72))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10402])).
% 1.71/1.64 tff(10404,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s72) | (~until21(s72)) | xuntil22(s72))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s72) | node20(s72) | (~until21(s72)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10403, 10401])).
% 1.71/1.64 tff(10405,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s72) | (~until21(s72)) | xuntil22(s72))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10406,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s72) | node20(s72) | (~until21(s72))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10405, 10404])).
% 1.71/1.64 tff(10407,plain,
% 1.71/1.64 (xuntil22(s72) | node20(s72)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10406, 9422, 10400])).
% 1.71/1.64 tff(10408,plain,
% 1.71/1.64 (xuntil22(s72)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10407, 8823])).
% 1.71/1.64 tff(10409,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s72, s73)) | (~xuntil22(s72)) | until21(s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s72, s73)) | (~xuntil22(s72)) | until21(s73))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10410,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s72, s73)) | (~xuntil22(s72)) | until21(s73))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10411,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s72, s73)) | (~xuntil22(s72)) | until21(s73)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10410, 10409])).
% 1.71/1.64 tff(10412,plain,
% 1.71/1.64 ((~xuntil22(s72)) | until21(s73)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10411, 6171, 9440])).
% 1.71/1.64 tff(10413,plain,
% 1.71/1.64 (until21(s73)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10412, 10408])).
% 1.71/1.64 tff(10414,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s73) | node20(s73) | (~until21(s73)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s73) | node20(s73) | (~until21(s73)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10415,plain,
% 1.71/1.64 ((node20(s73) | (~until21(s73)) | xuntil22(s73)) <=> (xuntil22(s73) | node20(s73) | (~until21(s73)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10416,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s73) | (~until21(s73)) | xuntil22(s73))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s73) | node20(s73) | (~until21(s73))))),
% 1.71/1.64 inference(monotonicity,[status(thm)],[10415])).
% 1.71/1.64 tff(10417,plain,
% 1.71/1.64 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s73) | (~until21(s73)) | xuntil22(s73))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s73) | node20(s73) | (~until21(s73)))),
% 1.71/1.64 inference(transitivity,[status(thm)],[10416, 10414])).
% 1.71/1.64 tff(10418,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s73) | (~until21(s73)) | xuntil22(s73))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10419,plain,
% 1.71/1.64 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s73) | node20(s73) | (~until21(s73))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10418, 10417])).
% 1.71/1.64 tff(10420,plain,
% 1.71/1.64 (xuntil22(s73)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10419, 9422, 10413, 8814])).
% 1.71/1.64 tff(10421,plain,
% 1.71/1.64 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s73, s74)) | (~xuntil22(s73)) | until21(s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s73, s74)) | (~xuntil22(s73)) | until21(s74))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10422,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s73, s74)) | (~xuntil22(s73)) | until21(s74))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10423,plain,
% 1.71/1.64 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s73, s74)) | (~xuntil22(s73)) | until21(s74)),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10422, 10421])).
% 1.71/1.64 tff(10424,plain,
% 1.71/1.64 ((~xuntil22(s73)) | until21(s74)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10423, 6238, 9440])).
% 1.71/1.64 tff(10425,plain,
% 1.71/1.64 (until21(s74)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10424, 10420])).
% 1.71/1.64 tff(10426,plain,
% 1.71/1.64 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s74) | (~node20(s74)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s74) | (~node20(s74)))),
% 1.71/1.64 inference(rewrite,[status(thm)],[])).
% 1.71/1.64 tff(10427,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s74) | (~node20(s74)))),
% 1.71/1.64 inference(quant_inst,[status(thm)],[])).
% 1.71/1.64 tff(10428,plain,
% 1.71/1.64 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s74) | (~node20(s74))),
% 1.71/1.64 inference(modus_ponens,[status(thm)],[10427, 10426])).
% 1.71/1.64 tff(10429,plain,
% 1.71/1.64 (~node20(s74)),
% 1.71/1.64 inference(unit_resolution,[status(thm)],[10428, 8579, 8805])).
% 1.71/1.65 tff(10430,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s74) | node20(s74) | (~until21(s74)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s74) | node20(s74) | (~until21(s74)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10431,plain,
% 1.71/1.65 ((node20(s74) | (~until21(s74)) | xuntil22(s74)) <=> (xuntil22(s74) | node20(s74) | (~until21(s74)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10432,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s74) | (~until21(s74)) | xuntil22(s74))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s74) | node20(s74) | (~until21(s74))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10431])).
% 1.71/1.65 tff(10433,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s74) | (~until21(s74)) | xuntil22(s74))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s74) | node20(s74) | (~until21(s74)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10432, 10430])).
% 1.71/1.65 tff(10434,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s74) | (~until21(s74)) | xuntil22(s74))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10435,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s74) | node20(s74) | (~until21(s74))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10434, 10433])).
% 1.71/1.65 tff(10436,plain,
% 1.71/1.65 (xuntil22(s74) | (~until21(s74))),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10435, 9422, 10429])).
% 1.71/1.65 tff(10437,plain,
% 1.71/1.65 (xuntil22(s74)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10436, 10425])).
% 1.71/1.65 tff(10438,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s74, s75)) | (~xuntil22(s74)) | until21(s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s74, s75)) | (~xuntil22(s74)) | until21(s75))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10439,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s74, s75)) | (~xuntil22(s74)) | until21(s75))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10440,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s74, s75)) | (~xuntil22(s74)) | until21(s75)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10439, 10438])).
% 1.71/1.65 tff(10441,plain,
% 1.71/1.65 ((~xuntil22(s74)) | until21(s75)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10440, 6337, 9440])).
% 1.71/1.65 tff(10442,plain,
% 1.71/1.65 (until21(s75)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10441, 10437])).
% 1.71/1.65 tff(10443,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s75) | node20(s75) | (~until21(s75)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s75) | node20(s75) | (~until21(s75)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10444,plain,
% 1.71/1.65 ((node20(s75) | (~until21(s75)) | xuntil22(s75)) <=> (xuntil22(s75) | node20(s75) | (~until21(s75)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10445,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s75) | (~until21(s75)) | xuntil22(s75))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s75) | node20(s75) | (~until21(s75))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10444])).
% 1.71/1.65 tff(10446,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s75) | (~until21(s75)) | xuntil22(s75))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s75) | node20(s75) | (~until21(s75)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10445, 10443])).
% 1.71/1.65 tff(10447,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s75) | (~until21(s75)) | xuntil22(s75))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10448,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s75) | node20(s75) | (~until21(s75))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10447, 10446])).
% 1.71/1.65 tff(10449,plain,
% 1.71/1.65 (xuntil22(s75)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10448, 9422, 10442, 8798])).
% 1.71/1.65 tff(10450,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s75, s76)) | (~xuntil22(s75)) | until21(s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s75, s76)) | (~xuntil22(s75)) | until21(s76))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10451,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s75, s76)) | (~xuntil22(s75)) | until21(s76))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10452,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s75, s76)) | (~xuntil22(s75)) | until21(s76)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10451, 10450])).
% 1.71/1.65 tff(10453,plain,
% 1.71/1.65 ((~xuntil22(s75)) | until21(s76)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10452, 6415, 9440])).
% 1.71/1.65 tff(10454,plain,
% 1.71/1.65 (until21(s76)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10453, 10449])).
% 1.71/1.65 tff(10455,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s76) | node20(s76) | (~until21(s76)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s76) | node20(s76) | (~until21(s76)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10456,plain,
% 1.71/1.65 ((node20(s76) | (~until21(s76)) | xuntil22(s76)) <=> (xuntil22(s76) | node20(s76) | (~until21(s76)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10457,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s76) | (~until21(s76)) | xuntil22(s76))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s76) | node20(s76) | (~until21(s76))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10456])).
% 1.71/1.65 tff(10458,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s76) | (~until21(s76)) | xuntil22(s76))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s76) | node20(s76) | (~until21(s76)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10457, 10455])).
% 1.71/1.65 tff(10459,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s76) | (~until21(s76)) | xuntil22(s76))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10460,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s76) | node20(s76) | (~until21(s76))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10459, 10458])).
% 1.71/1.65 tff(10461,plain,
% 1.71/1.65 (xuntil22(s76) | node20(s76)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10460, 9422, 10454])).
% 1.71/1.65 tff(10462,plain,
% 1.71/1.65 (xuntil22(s76)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10461, 8790])).
% 1.71/1.65 tff(10463,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s76, s77)) | (~xuntil22(s76)) | until21(s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s76, s77)) | (~xuntil22(s76)) | until21(s77))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10464,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s76, s77)) | (~xuntil22(s76)) | until21(s77))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10465,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s76, s77)) | (~xuntil22(s76)) | until21(s77)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10464, 10463])).
% 1.71/1.65 tff(10466,plain,
% 1.71/1.65 ((~xuntil22(s76)) | until21(s77)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10465, 6476, 9440])).
% 1.71/1.65 tff(10467,plain,
% 1.71/1.65 (until21(s77)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10466, 10462])).
% 1.71/1.65 tff(10468,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s77) | node20(s77) | (~until21(s77)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s77) | node20(s77) | (~until21(s77)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10469,plain,
% 1.71/1.65 ((node20(s77) | (~until21(s77)) | xuntil22(s77)) <=> (xuntil22(s77) | node20(s77) | (~until21(s77)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10470,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s77) | (~until21(s77)) | xuntil22(s77))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s77) | node20(s77) | (~until21(s77))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10469])).
% 1.71/1.65 tff(10471,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s77) | (~until21(s77)) | xuntil22(s77))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s77) | node20(s77) | (~until21(s77)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10470, 10468])).
% 1.71/1.65 tff(10472,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s77) | (~until21(s77)) | xuntil22(s77))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10473,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s77) | node20(s77) | (~until21(s77))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10472, 10471])).
% 1.71/1.65 tff(10474,plain,
% 1.71/1.65 (xuntil22(s77)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10473, 9422, 10467, 8781])).
% 1.71/1.65 tff(10475,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s77, s78)) | (~xuntil22(s77)) | until21(s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s77, s78)) | (~xuntil22(s77)) | until21(s78))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10476,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s77, s78)) | (~xuntil22(s77)) | until21(s78))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10477,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s77, s78)) | (~xuntil22(s77)) | until21(s78)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10476, 10475])).
% 1.71/1.65 tff(10478,plain,
% 1.71/1.65 ((~xuntil22(s77)) | until21(s78)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10477, 6571, 9440])).
% 1.71/1.65 tff(10479,plain,
% 1.71/1.65 (until21(s78)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10478, 10474])).
% 1.71/1.65 tff(10480,plain,
% 1.71/1.65 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s78) | (~node20(s78)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s78) | (~node20(s78)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10481,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s78) | (~node20(s78)))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10482,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s78) | (~node20(s78))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10481, 10480])).
% 1.71/1.65 tff(10483,plain,
% 1.71/1.65 (~node20(s78)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10482, 8579, 8772])).
% 1.71/1.65 tff(10484,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s78) | node20(s78) | (~until21(s78)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s78) | node20(s78) | (~until21(s78)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10485,plain,
% 1.71/1.65 ((node20(s78) | (~until21(s78)) | xuntil22(s78)) <=> (xuntil22(s78) | node20(s78) | (~until21(s78)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10486,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s78) | (~until21(s78)) | xuntil22(s78))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s78) | node20(s78) | (~until21(s78))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10485])).
% 1.71/1.65 tff(10487,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s78) | (~until21(s78)) | xuntil22(s78))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s78) | node20(s78) | (~until21(s78)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10486, 10484])).
% 1.71/1.65 tff(10488,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s78) | (~until21(s78)) | xuntil22(s78))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10489,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s78) | node20(s78) | (~until21(s78))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10488, 10487])).
% 1.71/1.65 tff(10490,plain,
% 1.71/1.65 (xuntil22(s78) | (~until21(s78))),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10489, 9422, 10483])).
% 1.71/1.65 tff(10491,plain,
% 1.71/1.65 (xuntil22(s78)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10490, 10479])).
% 1.71/1.65 tff(10492,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s78, s79)) | (~xuntil22(s78)) | until21(s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s78, s79)) | (~xuntil22(s78)) | until21(s79))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10493,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s78, s79)) | (~xuntil22(s78)) | until21(s79))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10494,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s78, s79)) | (~xuntil22(s78)) | until21(s79)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10493, 10492])).
% 1.71/1.65 tff(10495,plain,
% 1.71/1.65 ((~xuntil22(s78)) | until21(s79)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10494, 6635, 9440])).
% 1.71/1.65 tff(10496,plain,
% 1.71/1.65 (until21(s79)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10495, 10491])).
% 1.71/1.65 tff(10497,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s79) | node20(s79) | (~until21(s79)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s79) | node20(s79) | (~until21(s79)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10498,plain,
% 1.71/1.65 ((node20(s79) | (~until21(s79)) | xuntil22(s79)) <=> (xuntil22(s79) | node20(s79) | (~until21(s79)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10499,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s79) | (~until21(s79)) | xuntil22(s79))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s79) | node20(s79) | (~until21(s79))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10498])).
% 1.71/1.65 tff(10500,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s79) | (~until21(s79)) | xuntil22(s79))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s79) | node20(s79) | (~until21(s79)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10499, 10497])).
% 1.71/1.65 tff(10501,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s79) | (~until21(s79)) | xuntil22(s79))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10502,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s79) | node20(s79) | (~until21(s79))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10501, 10500])).
% 1.71/1.65 tff(10503,plain,
% 1.71/1.65 (xuntil22(s79)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10502, 9422, 10496, 8765])).
% 1.71/1.65 tff(10504,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s79, s80)) | (~xuntil22(s79)) | until21(s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s79, s80)) | (~xuntil22(s79)) | until21(s80))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10505,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s79, s80)) | (~xuntil22(s79)) | until21(s80))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10506,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s79, s80)) | (~xuntil22(s79)) | until21(s80)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10505, 10504])).
% 1.71/1.65 tff(10507,plain,
% 1.71/1.65 ((~xuntil22(s79)) | until21(s80)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10506, 6710, 9440])).
% 1.71/1.65 tff(10508,plain,
% 1.71/1.65 (until21(s80)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10507, 10503])).
% 1.71/1.65 tff(10509,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s80) | node20(s80) | (~until21(s80)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s80) | node20(s80) | (~until21(s80)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10510,plain,
% 1.71/1.65 ((node20(s80) | (~until21(s80)) | xuntil22(s80)) <=> (xuntil22(s80) | node20(s80) | (~until21(s80)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10511,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s80) | (~until21(s80)) | xuntil22(s80))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s80) | node20(s80) | (~until21(s80))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10510])).
% 1.71/1.65 tff(10512,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s80) | (~until21(s80)) | xuntil22(s80))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s80) | node20(s80) | (~until21(s80)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10511, 10509])).
% 1.71/1.65 tff(10513,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s80) | (~until21(s80)) | xuntil22(s80))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10514,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s80) | node20(s80) | (~until21(s80))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10513, 10512])).
% 1.71/1.65 tff(10515,plain,
% 1.71/1.65 (xuntil22(s80) | node20(s80)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10514, 9422, 10508])).
% 1.71/1.65 tff(10516,plain,
% 1.71/1.65 (xuntil22(s80)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10515, 8757])).
% 1.71/1.65 tff(10517,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s80, s81)) | (~xuntil22(s80)) | until21(s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s80, s81)) | (~xuntil22(s80)) | until21(s81))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10518,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s80, s81)) | (~xuntil22(s80)) | until21(s81))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10519,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s80, s81)) | (~xuntil22(s80)) | until21(s81)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10518, 10517])).
% 1.71/1.65 tff(10520,plain,
% 1.71/1.65 ((~xuntil22(s80)) | until21(s81)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10519, 6799, 9440])).
% 1.71/1.65 tff(10521,plain,
% 1.71/1.65 (until21(s81)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10520, 10516])).
% 1.71/1.65 tff(10522,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s81) | node20(s81) | (~until21(s81)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s81) | node20(s81) | (~until21(s81)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10523,plain,
% 1.71/1.65 ((node20(s81) | (~until21(s81)) | xuntil22(s81)) <=> (xuntil22(s81) | node20(s81) | (~until21(s81)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10524,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s81) | (~until21(s81)) | xuntil22(s81))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s81) | node20(s81) | (~until21(s81))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10523])).
% 1.71/1.65 tff(10525,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s81) | (~until21(s81)) | xuntil22(s81))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s81) | node20(s81) | (~until21(s81)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10524, 10522])).
% 1.71/1.65 tff(10526,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s81) | (~until21(s81)) | xuntil22(s81))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10527,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s81) | node20(s81) | (~until21(s81))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10526, 10525])).
% 1.71/1.65 tff(10528,plain,
% 1.71/1.65 (xuntil22(s81)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10527, 9422, 10521, 8748])).
% 1.71/1.65 tff(10529,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s81, s82)) | (~xuntil22(s81)) | until21(s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s81, s82)) | (~xuntil22(s81)) | until21(s82))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10530,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s81, s82)) | (~xuntil22(s81)) | until21(s82))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10531,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s81, s82)) | (~xuntil22(s81)) | until21(s82)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10530, 10529])).
% 1.71/1.65 tff(10532,plain,
% 1.71/1.65 ((~xuntil22(s81)) | until21(s82)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10531, 6866, 9440])).
% 1.71/1.65 tff(10533,plain,
% 1.71/1.65 (until21(s82)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10532, 10528])).
% 1.71/1.65 tff(10534,plain,
% 1.71/1.65 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s82) | (~node20(s82)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s82) | (~node20(s82)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10535,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s82) | (~node20(s82)))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10536,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s82) | (~node20(s82))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10535, 10534])).
% 1.71/1.65 tff(10537,plain,
% 1.71/1.65 (~node20(s82)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10536, 8579, 8739])).
% 1.71/1.65 tff(10538,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s82) | node20(s82) | (~until21(s82)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s82) | node20(s82) | (~until21(s82)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10539,plain,
% 1.71/1.65 ((node20(s82) | (~until21(s82)) | xuntil22(s82)) <=> (xuntil22(s82) | node20(s82) | (~until21(s82)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10540,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s82) | (~until21(s82)) | xuntil22(s82))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s82) | node20(s82) | (~until21(s82))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10539])).
% 1.71/1.65 tff(10541,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s82) | (~until21(s82)) | xuntil22(s82))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s82) | node20(s82) | (~until21(s82)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10540, 10538])).
% 1.71/1.65 tff(10542,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s82) | (~until21(s82)) | xuntil22(s82))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10543,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s82) | node20(s82) | (~until21(s82))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10542, 10541])).
% 1.71/1.65 tff(10544,plain,
% 1.71/1.65 (xuntil22(s82) | (~until21(s82))),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10543, 9422, 10537])).
% 1.71/1.65 tff(10545,plain,
% 1.71/1.65 (xuntil22(s82)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10544, 10533])).
% 1.71/1.65 tff(10546,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s82, s83)) | (~xuntil22(s82)) | until21(s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s82, s83)) | (~xuntil22(s82)) | until21(s83))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10547,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s82, s83)) | (~xuntil22(s82)) | until21(s83))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10548,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s82, s83)) | (~xuntil22(s82)) | until21(s83)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10547, 10546])).
% 1.71/1.65 tff(10549,plain,
% 1.71/1.65 ((~xuntil22(s82)) | until21(s83)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10548, 6965, 9440])).
% 1.71/1.65 tff(10550,plain,
% 1.71/1.65 (until21(s83)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10549, 10545])).
% 1.71/1.65 tff(10551,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s83) | node20(s83) | (~until21(s83)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s83) | node20(s83) | (~until21(s83)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10552,plain,
% 1.71/1.65 ((node20(s83) | (~until21(s83)) | xuntil22(s83)) <=> (xuntil22(s83) | node20(s83) | (~until21(s83)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10553,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s83) | (~until21(s83)) | xuntil22(s83))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s83) | node20(s83) | (~until21(s83))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10552])).
% 1.71/1.65 tff(10554,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s83) | (~until21(s83)) | xuntil22(s83))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s83) | node20(s83) | (~until21(s83)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10553, 10551])).
% 1.71/1.65 tff(10555,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s83) | (~until21(s83)) | xuntil22(s83))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10556,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s83) | node20(s83) | (~until21(s83))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10555, 10554])).
% 1.71/1.65 tff(10557,plain,
% 1.71/1.65 (xuntil22(s83)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10556, 9422, 10550, 8732])).
% 1.71/1.65 tff(10558,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s83, s84)) | (~xuntil22(s83)) | until21(s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s83, s84)) | (~xuntil22(s83)) | until21(s84))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10559,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s83, s84)) | (~xuntil22(s83)) | until21(s84))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10560,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s83, s84)) | (~xuntil22(s83)) | until21(s84)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10559, 10558])).
% 1.71/1.65 tff(10561,plain,
% 1.71/1.65 ((~xuntil22(s83)) | until21(s84)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10560, 7043, 9440])).
% 1.71/1.65 tff(10562,plain,
% 1.71/1.65 (until21(s84)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10561, 10557])).
% 1.71/1.65 tff(10563,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s84) | node20(s84) | (~until21(s84)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s84) | node20(s84) | (~until21(s84)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10564,plain,
% 1.71/1.65 ((node20(s84) | (~until21(s84)) | xuntil22(s84)) <=> (xuntil22(s84) | node20(s84) | (~until21(s84)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10565,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s84) | (~until21(s84)) | xuntil22(s84))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s84) | node20(s84) | (~until21(s84))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10564])).
% 1.71/1.65 tff(10566,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s84) | (~until21(s84)) | xuntil22(s84))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s84) | node20(s84) | (~until21(s84)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10565, 10563])).
% 1.71/1.65 tff(10567,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s84) | (~until21(s84)) | xuntil22(s84))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10568,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s84) | node20(s84) | (~until21(s84))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10567, 10566])).
% 1.71/1.65 tff(10569,plain,
% 1.71/1.65 (xuntil22(s84) | node20(s84)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10568, 9422, 10562])).
% 1.71/1.65 tff(10570,plain,
% 1.71/1.65 (xuntil22(s84)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10569, 8724])).
% 1.71/1.65 tff(10571,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s84, s85)) | (~xuntil22(s84)) | until21(s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s84, s85)) | (~xuntil22(s84)) | until21(s85))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10572,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s84, s85)) | (~xuntil22(s84)) | until21(s85))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10573,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s84, s85)) | (~xuntil22(s84)) | until21(s85)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10572, 10571])).
% 1.71/1.65 tff(10574,plain,
% 1.71/1.65 ((~xuntil22(s84)) | until21(s85)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10573, 7104, 9440])).
% 1.71/1.65 tff(10575,plain,
% 1.71/1.65 (until21(s85)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10574, 10570])).
% 1.71/1.65 tff(10576,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s85) | node20(s85) | (~until21(s85)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s85) | node20(s85) | (~until21(s85)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10577,plain,
% 1.71/1.65 ((node20(s85) | (~until21(s85)) | xuntil22(s85)) <=> (xuntil22(s85) | node20(s85) | (~until21(s85)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10578,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s85) | (~until21(s85)) | xuntil22(s85))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s85) | node20(s85) | (~until21(s85))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10577])).
% 1.71/1.65 tff(10579,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s85) | (~until21(s85)) | xuntil22(s85))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s85) | node20(s85) | (~until21(s85)))),
% 1.71/1.65 inference(transitivity,[status(thm)],[10578, 10576])).
% 1.71/1.65 tff(10580,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s85) | (~until21(s85)) | xuntil22(s85))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10581,plain,
% 1.71/1.65 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s85) | node20(s85) | (~until21(s85))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10580, 10579])).
% 1.71/1.65 tff(10582,plain,
% 1.71/1.65 (xuntil22(s85)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10581, 9422, 10575, 8715])).
% 1.71/1.65 tff(10583,plain,
% 1.71/1.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s85, s86)) | (~xuntil22(s85)) | until21(s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s85, s86)) | (~xuntil22(s85)) | until21(s86))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10584,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s85, s86)) | (~xuntil22(s85)) | until21(s86))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10585,plain,
% 1.71/1.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s85, s86)) | (~xuntil22(s85)) | until21(s86)),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10584, 10583])).
% 1.71/1.65 tff(10586,plain,
% 1.71/1.65 ((~xuntil22(s85)) | until21(s86)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10585, 7199, 9440])).
% 1.71/1.65 tff(10587,plain,
% 1.71/1.65 (until21(s86)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10586, 10582])).
% 1.71/1.65 tff(10588,plain,
% 1.71/1.65 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s86) | (~node20(s86)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s86) | (~node20(s86)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10589,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s86) | (~node20(s86)))),
% 1.71/1.65 inference(quant_inst,[status(thm)],[])).
% 1.71/1.65 tff(10590,plain,
% 1.71/1.65 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s86) | (~node20(s86))),
% 1.71/1.65 inference(modus_ponens,[status(thm)],[10589, 10588])).
% 1.71/1.65 tff(10591,plain,
% 1.71/1.65 (~node20(s86)),
% 1.71/1.65 inference(unit_resolution,[status(thm)],[10590, 8579, 8706])).
% 1.71/1.65 tff(10592,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s86) | node20(s86) | (~until21(s86)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s86) | node20(s86) | (~until21(s86)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10593,plain,
% 1.71/1.65 ((node20(s86) | (~until21(s86)) | xuntil22(s86)) <=> (xuntil22(s86) | node20(s86) | (~until21(s86)))),
% 1.71/1.65 inference(rewrite,[status(thm)],[])).
% 1.71/1.65 tff(10594,plain,
% 1.71/1.65 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s86) | (~until21(s86)) | xuntil22(s86))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s86) | node20(s86) | (~until21(s86))))),
% 1.71/1.65 inference(monotonicity,[status(thm)],[10593])).
% 1.71/1.66 tff(10595,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s86) | (~until21(s86)) | xuntil22(s86))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s86) | node20(s86) | (~until21(s86)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10594, 10592])).
% 1.71/1.66 tff(10596,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s86) | (~until21(s86)) | xuntil22(s86))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10597,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s86) | node20(s86) | (~until21(s86))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10596, 10595])).
% 1.71/1.66 tff(10598,plain,
% 1.71/1.66 (xuntil22(s86) | (~until21(s86))),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10597, 9422, 10591])).
% 1.71/1.66 tff(10599,plain,
% 1.71/1.66 (xuntil22(s86)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10598, 10587])).
% 1.71/1.66 tff(10600,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s86, s87)) | (~xuntil22(s86)) | until21(s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s86, s87)) | (~xuntil22(s86)) | until21(s87))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10601,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s86, s87)) | (~xuntil22(s86)) | until21(s87))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10602,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s86, s87)) | (~xuntil22(s86)) | until21(s87)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10601, 10600])).
% 1.71/1.66 tff(10603,plain,
% 1.71/1.66 ((~xuntil22(s86)) | until21(s87)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10602, 7263, 9440])).
% 1.71/1.66 tff(10604,plain,
% 1.71/1.66 (until21(s87)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10603, 10599])).
% 1.71/1.66 tff(10605,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s87) | node20(s87) | (~until21(s87)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s87) | node20(s87) | (~until21(s87)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10606,plain,
% 1.71/1.66 ((node20(s87) | (~until21(s87)) | xuntil22(s87)) <=> (xuntil22(s87) | node20(s87) | (~until21(s87)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10607,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s87) | (~until21(s87)) | xuntil22(s87))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s87) | node20(s87) | (~until21(s87))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10606])).
% 1.71/1.66 tff(10608,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s87) | (~until21(s87)) | xuntil22(s87))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s87) | node20(s87) | (~until21(s87)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10607, 10605])).
% 1.71/1.66 tff(10609,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s87) | (~until21(s87)) | xuntil22(s87))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10610,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s87) | node20(s87) | (~until21(s87))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10609, 10608])).
% 1.71/1.66 tff(10611,plain,
% 1.71/1.66 (xuntil22(s87)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10610, 9422, 10604, 8699])).
% 1.71/1.66 tff(10612,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s87, s88)) | (~xuntil22(s87)) | until21(s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s87, s88)) | (~xuntil22(s87)) | until21(s88))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10613,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s87, s88)) | (~xuntil22(s87)) | until21(s88))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10614,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s87, s88)) | (~xuntil22(s87)) | until21(s88)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10613, 10612])).
% 1.71/1.66 tff(10615,plain,
% 1.71/1.66 ((~xuntil22(s87)) | until21(s88)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10614, 7338, 9440])).
% 1.71/1.66 tff(10616,plain,
% 1.71/1.66 (until21(s88)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10615, 10611])).
% 1.71/1.66 tff(10617,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s88) | node20(s88) | (~until21(s88)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s88) | node20(s88) | (~until21(s88)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10618,plain,
% 1.71/1.66 ((node20(s88) | (~until21(s88)) | xuntil22(s88)) <=> (xuntil22(s88) | node20(s88) | (~until21(s88)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10619,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s88) | (~until21(s88)) | xuntil22(s88))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s88) | node20(s88) | (~until21(s88))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10618])).
% 1.71/1.66 tff(10620,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s88) | (~until21(s88)) | xuntil22(s88))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s88) | node20(s88) | (~until21(s88)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10619, 10617])).
% 1.71/1.66 tff(10621,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s88) | (~until21(s88)) | xuntil22(s88))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10622,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s88) | node20(s88) | (~until21(s88))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 1.71/1.66 tff(10623,plain,
% 1.71/1.66 (xuntil22(s88) | node20(s88)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10622, 9422, 10616])).
% 1.71/1.66 tff(10624,plain,
% 1.71/1.66 (xuntil22(s88)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10623, 8691])).
% 1.71/1.66 tff(10625,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s88, s89)) | (~xuntil22(s88)) | until21(s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s88, s89)) | (~xuntil22(s88)) | until21(s89))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10626,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s88, s89)) | (~xuntil22(s88)) | until21(s89))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10627,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s88, s89)) | (~xuntil22(s88)) | until21(s89)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10626, 10625])).
% 1.71/1.66 tff(10628,plain,
% 1.71/1.66 ((~xuntil22(s88)) | until21(s89)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10627, 7427, 9440])).
% 1.71/1.66 tff(10629,plain,
% 1.71/1.66 (until21(s89)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10628, 10624])).
% 1.71/1.66 tff(10630,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s89) | node20(s89) | (~until21(s89)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s89) | node20(s89) | (~until21(s89)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10631,plain,
% 1.71/1.66 ((node20(s89) | (~until21(s89)) | xuntil22(s89)) <=> (xuntil22(s89) | node20(s89) | (~until21(s89)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10632,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s89) | (~until21(s89)) | xuntil22(s89))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s89) | node20(s89) | (~until21(s89))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10631])).
% 1.71/1.66 tff(10633,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s89) | (~until21(s89)) | xuntil22(s89))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s89) | node20(s89) | (~until21(s89)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10632, 10630])).
% 1.71/1.66 tff(10634,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s89) | (~until21(s89)) | xuntil22(s89))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10635,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s89) | node20(s89) | (~until21(s89))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10634, 10633])).
% 1.71/1.66 tff(10636,plain,
% 1.71/1.66 (xuntil22(s89)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10635, 9422, 10629, 8682])).
% 1.71/1.66 tff(10637,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s89, s90)) | (~xuntil22(s89)) | until21(s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s89, s90)) | (~xuntil22(s89)) | until21(s90))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10638,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s89, s90)) | (~xuntil22(s89)) | until21(s90))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10639,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s89, s90)) | (~xuntil22(s89)) | until21(s90)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10638, 10637])).
% 1.71/1.66 tff(10640,plain,
% 1.71/1.66 ((~xuntil22(s89)) | until21(s90)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10639, 7494, 9440])).
% 1.71/1.66 tff(10641,plain,
% 1.71/1.66 (until21(s90)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10640, 10636])).
% 1.71/1.66 tff(10642,plain,
% 1.71/1.66 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s90) | (~node20(s90)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s90) | (~node20(s90)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10643,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s90) | (~node20(s90)))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10644,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s90) | (~node20(s90))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10643, 10642])).
% 1.71/1.66 tff(10645,plain,
% 1.71/1.66 (~node20(s90)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10644, 8579, 8673])).
% 1.71/1.66 tff(10646,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s90) | node20(s90) | (~until21(s90)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s90) | node20(s90) | (~until21(s90)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10647,plain,
% 1.71/1.66 ((node20(s90) | (~until21(s90)) | xuntil22(s90)) <=> (xuntil22(s90) | node20(s90) | (~until21(s90)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10648,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s90) | (~until21(s90)) | xuntil22(s90))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s90) | node20(s90) | (~until21(s90))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10647])).
% 1.71/1.66 tff(10649,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s90) | (~until21(s90)) | xuntil22(s90))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s90) | node20(s90) | (~until21(s90)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10648, 10646])).
% 1.71/1.66 tff(10650,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s90) | (~until21(s90)) | xuntil22(s90))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10651,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s90) | node20(s90) | (~until21(s90))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10650, 10649])).
% 1.71/1.66 tff(10652,plain,
% 1.71/1.66 (xuntil22(s90) | (~until21(s90))),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10651, 9422, 10645])).
% 1.71/1.66 tff(10653,plain,
% 1.71/1.66 (xuntil22(s90)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10652, 10641])).
% 1.71/1.66 tff(10654,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s90, s91)) | (~xuntil22(s90)) | until21(s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s90, s91)) | (~xuntil22(s90)) | until21(s91))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10655,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s90, s91)) | (~xuntil22(s90)) | until21(s91))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10656,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s90, s91)) | (~xuntil22(s90)) | until21(s91)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10655, 10654])).
% 1.71/1.66 tff(10657,plain,
% 1.71/1.66 ((~xuntil22(s90)) | until21(s91)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10656, 7593, 9440])).
% 1.71/1.66 tff(10658,plain,
% 1.71/1.66 (until21(s91)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10657, 10653])).
% 1.71/1.66 tff(10659,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s91) | node20(s91) | (~until21(s91)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s91) | node20(s91) | (~until21(s91)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10660,plain,
% 1.71/1.66 ((node20(s91) | (~until21(s91)) | xuntil22(s91)) <=> (xuntil22(s91) | node20(s91) | (~until21(s91)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10661,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s91) | (~until21(s91)) | xuntil22(s91))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s91) | node20(s91) | (~until21(s91))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10660])).
% 1.71/1.66 tff(10662,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s91) | (~until21(s91)) | xuntil22(s91))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s91) | node20(s91) | (~until21(s91)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10661, 10659])).
% 1.71/1.66 tff(10663,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s91) | (~until21(s91)) | xuntil22(s91))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10664,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s91) | node20(s91) | (~until21(s91))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10663, 10662])).
% 1.71/1.66 tff(10665,plain,
% 1.71/1.66 (xuntil22(s91)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10664, 9422, 10658, 8666])).
% 1.71/1.66 tff(10666,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s91, s92)) | (~xuntil22(s91)) | until21(s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s91, s92)) | (~xuntil22(s91)) | until21(s92))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10667,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s91, s92)) | (~xuntil22(s91)) | until21(s92))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10668,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s91, s92)) | (~xuntil22(s91)) | until21(s92)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10667, 10666])).
% 1.71/1.66 tff(10669,plain,
% 1.71/1.66 ((~xuntil22(s91)) | until21(s92)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10668, 7671, 9440])).
% 1.71/1.66 tff(10670,plain,
% 1.71/1.66 (until21(s92)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10669, 10665])).
% 1.71/1.66 tff(10671,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s92) | node20(s92) | (~until21(s92)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s92) | node20(s92) | (~until21(s92)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10672,plain,
% 1.71/1.66 ((node20(s92) | (~until21(s92)) | xuntil22(s92)) <=> (xuntil22(s92) | node20(s92) | (~until21(s92)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10673,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s92) | (~until21(s92)) | xuntil22(s92))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s92) | node20(s92) | (~until21(s92))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10672])).
% 1.71/1.66 tff(10674,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s92) | (~until21(s92)) | xuntil22(s92))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s92) | node20(s92) | (~until21(s92)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10673, 10671])).
% 1.71/1.66 tff(10675,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s92) | (~until21(s92)) | xuntil22(s92))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10676,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s92) | node20(s92) | (~until21(s92))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10675, 10674])).
% 1.71/1.66 tff(10677,plain,
% 1.71/1.66 (xuntil22(s92) | node20(s92)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10676, 9422, 10670])).
% 1.71/1.66 tff(10678,plain,
% 1.71/1.66 (xuntil22(s92)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10677, 8658])).
% 1.71/1.66 tff(10679,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s92, s93)) | (~xuntil22(s92)) | until21(s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s92, s93)) | (~xuntil22(s92)) | until21(s93))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10680,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s92, s93)) | (~xuntil22(s92)) | until21(s93))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10681,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s92, s93)) | (~xuntil22(s92)) | until21(s93)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10680, 10679])).
% 1.71/1.66 tff(10682,plain,
% 1.71/1.66 ((~xuntil22(s92)) | until21(s93)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10681, 7732, 9440])).
% 1.71/1.66 tff(10683,plain,
% 1.71/1.66 (until21(s93)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10682, 10678])).
% 1.71/1.66 tff(10684,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s93) | node20(s93) | (~until21(s93)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s93) | node20(s93) | (~until21(s93)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10685,plain,
% 1.71/1.66 ((node20(s93) | (~until21(s93)) | xuntil22(s93)) <=> (xuntil22(s93) | node20(s93) | (~until21(s93)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10686,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s93) | (~until21(s93)) | xuntil22(s93))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s93) | node20(s93) | (~until21(s93))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10685])).
% 1.71/1.66 tff(10687,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s93) | (~until21(s93)) | xuntil22(s93))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s93) | node20(s93) | (~until21(s93)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10686, 10684])).
% 1.71/1.66 tff(10688,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s93) | (~until21(s93)) | xuntil22(s93))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10689,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s93) | node20(s93) | (~until21(s93))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10688, 10687])).
% 1.71/1.66 tff(10690,plain,
% 1.71/1.66 (xuntil22(s93)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10689, 9422, 10683, 8649])).
% 1.71/1.66 tff(10691,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s93, s94)) | (~xuntil22(s93)) | until21(s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s93, s94)) | (~xuntil22(s93)) | until21(s94))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10692,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s93, s94)) | (~xuntil22(s93)) | until21(s94))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10693,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s93, s94)) | (~xuntil22(s93)) | until21(s94)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10692, 10691])).
% 1.71/1.66 tff(10694,plain,
% 1.71/1.66 ((~xuntil22(s93)) | until21(s94)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10693, 7827, 9440])).
% 1.71/1.66 tff(10695,plain,
% 1.71/1.66 (until21(s94)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10694, 10690])).
% 1.71/1.66 tff(10696,plain,
% 1.71/1.66 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s94) | (~node20(s94)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s94) | (~node20(s94)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10697,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s94) | (~node20(s94)))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10698,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s94) | (~node20(s94))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10697, 10696])).
% 1.71/1.66 tff(10699,plain,
% 1.71/1.66 (~node20(s94)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10698, 8579, 8640])).
% 1.71/1.66 tff(10700,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s94) | node20(s94) | (~until21(s94)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s94) | node20(s94) | (~until21(s94)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10701,plain,
% 1.71/1.66 ((node20(s94) | (~until21(s94)) | xuntil22(s94)) <=> (xuntil22(s94) | node20(s94) | (~until21(s94)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10702,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s94) | (~until21(s94)) | xuntil22(s94))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s94) | node20(s94) | (~until21(s94))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10701])).
% 1.71/1.66 tff(10703,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s94) | (~until21(s94)) | xuntil22(s94))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s94) | node20(s94) | (~until21(s94)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10702, 10700])).
% 1.71/1.66 tff(10704,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s94) | (~until21(s94)) | xuntil22(s94))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10705,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s94) | node20(s94) | (~until21(s94))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10704, 10703])).
% 1.71/1.66 tff(10706,plain,
% 1.71/1.66 (xuntil22(s94) | (~until21(s94))),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10705, 9422, 10699])).
% 1.71/1.66 tff(10707,plain,
% 1.71/1.66 (xuntil22(s94)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10706, 10695])).
% 1.71/1.66 tff(10708,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s94, s95)) | (~xuntil22(s94)) | until21(s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s94, s95)) | (~xuntil22(s94)) | until21(s95))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10709,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s94, s95)) | (~xuntil22(s94)) | until21(s95))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10710,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s94, s95)) | (~xuntil22(s94)) | until21(s95)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10709, 10708])).
% 1.71/1.66 tff(10711,plain,
% 1.71/1.66 ((~xuntil22(s94)) | until21(s95)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10710, 7891, 9440])).
% 1.71/1.66 tff(10712,plain,
% 1.71/1.66 (until21(s95)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10711, 10707])).
% 1.71/1.66 tff(10713,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s95) | node20(s95) | (~until21(s95)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s95) | node20(s95) | (~until21(s95)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10714,plain,
% 1.71/1.66 ((node20(s95) | (~until21(s95)) | xuntil22(s95)) <=> (xuntil22(s95) | node20(s95) | (~until21(s95)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10715,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s95) | (~until21(s95)) | xuntil22(s95))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s95) | node20(s95) | (~until21(s95))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10714])).
% 1.71/1.66 tff(10716,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s95) | (~until21(s95)) | xuntil22(s95))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s95) | node20(s95) | (~until21(s95)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10715, 10713])).
% 1.71/1.66 tff(10717,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s95) | (~until21(s95)) | xuntil22(s95))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10718,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s95) | node20(s95) | (~until21(s95))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10717, 10716])).
% 1.71/1.66 tff(10719,plain,
% 1.71/1.66 (xuntil22(s95)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10718, 9422, 10712, 8633])).
% 1.71/1.66 tff(10720,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s95, s96)) | (~xuntil22(s95)) | until21(s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s95, s96)) | (~xuntil22(s95)) | until21(s96))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10721,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s95, s96)) | (~xuntil22(s95)) | until21(s96))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10722,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s95, s96)) | (~xuntil22(s95)) | until21(s96)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10721, 10720])).
% 1.71/1.66 tff(10723,plain,
% 1.71/1.66 ((~xuntil22(s95)) | until21(s96)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10722, 7966, 9440])).
% 1.71/1.66 tff(10724,plain,
% 1.71/1.66 (until21(s96)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10723, 10719])).
% 1.71/1.66 tff(10725,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s96) | node20(s96) | (~until21(s96)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s96) | node20(s96) | (~until21(s96)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10726,plain,
% 1.71/1.66 ((node20(s96) | (~until21(s96)) | xuntil22(s96)) <=> (xuntil22(s96) | node20(s96) | (~until21(s96)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10727,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s96) | (~until21(s96)) | xuntil22(s96))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s96) | node20(s96) | (~until21(s96))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10726])).
% 1.71/1.66 tff(10728,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s96) | (~until21(s96)) | xuntil22(s96))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s96) | node20(s96) | (~until21(s96)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10727, 10725])).
% 1.71/1.66 tff(10729,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s96) | (~until21(s96)) | xuntil22(s96))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10730,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s96) | node20(s96) | (~until21(s96))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10729, 10728])).
% 1.71/1.66 tff(10731,plain,
% 1.71/1.66 (xuntil22(s96) | node20(s96)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10730, 9422, 10724])).
% 1.71/1.66 tff(10732,plain,
% 1.71/1.66 (xuntil22(s96)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10731, 8625])).
% 1.71/1.66 tff(10733,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s96, s97)) | (~xuntil22(s96)) | until21(s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s96, s97)) | (~xuntil22(s96)) | until21(s97))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10734,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s96, s97)) | (~xuntil22(s96)) | until21(s97))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10735,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s96, s97)) | (~xuntil22(s96)) | until21(s97)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10734, 10733])).
% 1.71/1.66 tff(10736,plain,
% 1.71/1.66 ((~xuntil22(s96)) | until21(s97)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10735, 8055, 9440])).
% 1.71/1.66 tff(10737,plain,
% 1.71/1.66 (until21(s97)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10736, 10732])).
% 1.71/1.66 tff(10738,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s97) | node20(s97) | (~until21(s97)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s97) | node20(s97) | (~until21(s97)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10739,plain,
% 1.71/1.66 ((node20(s97) | (~until21(s97)) | xuntil22(s97)) <=> (xuntil22(s97) | node20(s97) | (~until21(s97)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10740,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s97) | (~until21(s97)) | xuntil22(s97))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s97) | node20(s97) | (~until21(s97))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10739])).
% 1.71/1.66 tff(10741,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s97) | (~until21(s97)) | xuntil22(s97))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s97) | node20(s97) | (~until21(s97)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10740, 10738])).
% 1.71/1.66 tff(10742,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s97) | (~until21(s97)) | xuntil22(s97))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10743,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s97) | node20(s97) | (~until21(s97))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10742, 10741])).
% 1.71/1.66 tff(10744,plain,
% 1.71/1.66 (xuntil22(s97)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10743, 9422, 10737, 8616])).
% 1.71/1.66 tff(10745,plain,
% 1.71/1.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s97, s98)) | (~xuntil22(s97)) | until21(s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s97, s98)) | (~xuntil22(s97)) | until21(s98))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10746,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s97, s98)) | (~xuntil22(s97)) | until21(s98))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10747,plain,
% 1.71/1.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s97, s98)) | (~xuntil22(s97)) | until21(s98)),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10746, 10745])).
% 1.71/1.66 tff(10748,plain,
% 1.71/1.66 ((~xuntil22(s97)) | until21(s98)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10747, 8122, 9440])).
% 1.71/1.66 tff(10749,plain,
% 1.71/1.66 (until21(s98)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10748, 10744])).
% 1.71/1.66 tff(10750,plain,
% 1.71/1.66 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s98) | (~node20(s98)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s98) | (~node20(s98)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10751,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s98) | (~node20(s98)))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10752,plain,
% 1.71/1.66 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s98) | (~node20(s98))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10751, 10750])).
% 1.71/1.66 tff(10753,plain,
% 1.71/1.66 (~node20(s98)),
% 1.71/1.66 inference(unit_resolution,[status(thm)],[10752, 8579, 8607])).
% 1.71/1.66 tff(10754,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s98) | node20(s98) | (~until21(s98)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s98) | node20(s98) | (~until21(s98)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10755,plain,
% 1.71/1.66 ((node20(s98) | (~until21(s98)) | xuntil22(s98)) <=> (xuntil22(s98) | node20(s98) | (~until21(s98)))),
% 1.71/1.66 inference(rewrite,[status(thm)],[])).
% 1.71/1.66 tff(10756,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s98) | (~until21(s98)) | xuntil22(s98))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s98) | node20(s98) | (~until21(s98))))),
% 1.71/1.66 inference(monotonicity,[status(thm)],[10755])).
% 1.71/1.66 tff(10757,plain,
% 1.71/1.66 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s98) | (~until21(s98)) | xuntil22(s98))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s98) | node20(s98) | (~until21(s98)))),
% 1.71/1.66 inference(transitivity,[status(thm)],[10756, 10754])).
% 1.71/1.66 tff(10758,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s98) | (~until21(s98)) | xuntil22(s98))),
% 1.71/1.66 inference(quant_inst,[status(thm)],[])).
% 1.71/1.66 tff(10759,plain,
% 1.71/1.66 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s98) | node20(s98) | (~until21(s98))),
% 1.71/1.66 inference(modus_ponens,[status(thm)],[10758, 10757])).
% 1.71/1.67 tff(10760,plain,
% 1.71/1.67 (xuntil22(s98) | (~until21(s98))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10759, 9422, 10753])).
% 1.71/1.67 tff(10761,plain,
% 1.71/1.67 (xuntil22(s98)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10760, 10749])).
% 1.71/1.67 tff(10762,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s98, s99)) | (~xuntil22(s98)) | until21(s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s98, s99)) | (~xuntil22(s98)) | until21(s99))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10763,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s98, s99)) | (~xuntil22(s98)) | until21(s99))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10764,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s98, s99)) | (~xuntil22(s98)) | until21(s99)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10763, 10762])).
% 1.71/1.67 tff(10765,plain,
% 1.71/1.67 ((~xuntil22(s98)) | until21(s99)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10764, 8221, 9440])).
% 1.71/1.67 tff(10766,plain,
% 1.71/1.67 (until21(s99)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10765, 10761])).
% 1.71/1.67 tff(10767,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s99) | node20(s99) | (~until21(s99)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s99) | node20(s99) | (~until21(s99)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10768,plain,
% 1.71/1.67 ((node20(s99) | (~until21(s99)) | xuntil22(s99)) <=> (xuntil22(s99) | node20(s99) | (~until21(s99)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10769,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s99) | (~until21(s99)) | xuntil22(s99))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s99) | node20(s99) | (~until21(s99))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10768])).
% 1.71/1.67 tff(10770,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s99) | (~until21(s99)) | xuntil22(s99))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s99) | node20(s99) | (~until21(s99)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10769, 10767])).
% 1.71/1.67 tff(10771,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s99) | (~until21(s99)) | xuntil22(s99))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10772,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s99) | node20(s99) | (~until21(s99))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10771, 10770])).
% 1.71/1.67 tff(10773,plain,
% 1.71/1.67 (xuntil22(s99)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10772, 9422, 10766, 8600])).
% 1.71/1.67 tff(10774,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s99, s100)) | (~xuntil22(s99)) | until21(s100))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s99, s100)) | (~xuntil22(s99)) | until21(s100))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10775,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s99, s100)) | (~xuntil22(s99)) | until21(s100))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10776,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s99, s100)) | (~xuntil22(s99)) | until21(s100)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10775, 10774])).
% 1.71/1.67 tff(10777,plain,
% 1.71/1.67 ((~xuntil22(s99)) | until21(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10776, 8299, 9440])).
% 1.71/1.67 tff(10778,plain,
% 1.71/1.67 (until21(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10777, 10773])).
% 1.71/1.67 tff(10779,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s100) | node20(s100) | (~until21(s100)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s100) | node20(s100) | (~until21(s100)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10780,plain,
% 1.71/1.67 ((node20(s100) | (~until21(s100)) | xuntil22(s100)) <=> (xuntil22(s100) | node20(s100) | (~until21(s100)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10781,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s100) | (~until21(s100)) | xuntil22(s100))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s100) | node20(s100) | (~until21(s100))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10780])).
% 1.71/1.67 tff(10782,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s100) | (~until21(s100)) | xuntil22(s100))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s100) | node20(s100) | (~until21(s100)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10781, 10779])).
% 1.71/1.67 tff(10783,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s100) | (~until21(s100)) | xuntil22(s100))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10784,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s100) | node20(s100) | (~until21(s100))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10783, 10782])).
% 1.71/1.67 tff(10785,plain,
% 1.71/1.67 (xuntil22(s100) | node20(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10784, 9422, 10778])).
% 1.71/1.67 tff(10786,plain,
% 1.71/1.67 (xuntil22(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10785, 8592])).
% 1.71/1.67 tff(10787,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s100, s101)) | (~xuntil22(s100)) | until21(s101))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s100, s101)) | (~xuntil22(s100)) | until21(s101))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10788,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s100, s101)) | (~xuntil22(s100)) | until21(s101))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10789,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s100, s101)) | (~xuntil22(s100)) | until21(s101)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10788, 10787])).
% 1.71/1.67 tff(10790,plain,
% 1.71/1.67 ((~xuntil22(s100)) | until21(s101)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10789, 8360, 9440])).
% 1.71/1.67 tff(10791,plain,
% 1.71/1.67 (until21(s101)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10790, 10786])).
% 1.71/1.67 tff(10792,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s101) | node20(s101) | (~until21(s101)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s101) | node20(s101) | (~until21(s101)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10793,plain,
% 1.71/1.67 ((node20(s101) | (~until21(s101)) | xuntil22(s101)) <=> (xuntil22(s101) | node20(s101) | (~until21(s101)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10794,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s101) | (~until21(s101)) | xuntil22(s101))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s101) | node20(s101) | (~until21(s101))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10793])).
% 1.71/1.67 tff(10795,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s101) | (~until21(s101)) | xuntil22(s101))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s101) | node20(s101) | (~until21(s101)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10794, 10792])).
% 1.71/1.67 tff(10796,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s101) | (~until21(s101)) | xuntil22(s101))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10797,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s101) | node20(s101) | (~until21(s101))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10796, 10795])).
% 1.71/1.67 tff(10798,plain,
% 1.71/1.67 (xuntil22(s101)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10797, 9422, 10791, 8583])).
% 1.71/1.67 tff(10799,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s101, s102)) | (~xuntil22(s101)) | until21(s102))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s101, s102)) | (~xuntil22(s101)) | until21(s102))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10800,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s101, s102)) | (~xuntil22(s101)) | until21(s102))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10801,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s101, s102)) | (~xuntil22(s101)) | until21(s102)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10800, 10799])).
% 1.71/1.67 tff(10802,plain,
% 1.71/1.67 ((~xuntil22(s101)) | until21(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10801, 8455, 9440])).
% 1.71/1.67 tff(10803,plain,
% 1.71/1.67 (until21(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10802, 10798])).
% 1.71/1.67 tff(10804,plain,
% 1.71/1.67 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s102) | (~node20(s102)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s102) | (~node20(s102)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10805,plain,
% 1.71/1.67 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s102) | (~node20(s102)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10806,plain,
% 1.71/1.67 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s102) | (~node20(s102))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10805, 10804])).
% 1.71/1.67 tff(10807,plain,
% 1.71/1.67 (~node20(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10806, 8579, 8557])).
% 1.71/1.67 tff(10808,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s102) | node20(s102) | (~until21(s102)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s102) | node20(s102) | (~until21(s102)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10809,plain,
% 1.71/1.67 ((node20(s102) | (~until21(s102)) | xuntil22(s102)) <=> (xuntil22(s102) | node20(s102) | (~until21(s102)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10810,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s102) | (~until21(s102)) | xuntil22(s102))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s102) | node20(s102) | (~until21(s102))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10809])).
% 1.71/1.67 tff(10811,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s102) | (~until21(s102)) | xuntil22(s102))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s102) | node20(s102) | (~until21(s102)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10810, 10808])).
% 1.71/1.67 tff(10812,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s102) | (~until21(s102)) | xuntil22(s102))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10813,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s102) | node20(s102) | (~until21(s102))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10812, 10811])).
% 1.71/1.67 tff(10814,plain,
% 1.71/1.67 (xuntil22(s102) | (~until21(s102))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10813, 9422, 10807])).
% 1.71/1.67 tff(10815,plain,
% 1.71/1.67 (xuntil22(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10814, 10803])).
% 1.71/1.67 tff(10816,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s102, s103)) | (~xuntil22(s102)) | until21(s103))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s102, s103)) | (~xuntil22(s102)) | until21(s103))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10817,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s102, s103)) | (~xuntil22(s102)) | until21(s103))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10818,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s102, s103)) | (~xuntil22(s102)) | until21(s103)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10817, 10816])).
% 1.71/1.67 tff(10819,plain,
% 1.71/1.67 ((~xuntil22(s102)) | until21(s103)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10818, 8519, 9440])).
% 1.71/1.67 tff(10820,plain,
% 1.71/1.67 (until21(s103)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10819, 10815])).
% 1.71/1.67 tff(10821,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s103) | node20(s103) | (~until21(s103)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s103) | node20(s103) | (~until21(s103)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10822,plain,
% 1.71/1.67 ((node20(s103) | (~until21(s103)) | xuntil22(s103)) <=> (xuntil22(s103) | node20(s103) | (~until21(s103)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10823,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s103) | (~until21(s103)) | xuntil22(s103))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s103) | node20(s103) | (~until21(s103))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10822])).
% 1.71/1.67 tff(10824,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s103) | (~until21(s103)) | xuntil22(s103))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s103) | node20(s103) | (~until21(s103)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10823, 10821])).
% 1.71/1.67 tff(10825,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s103) | (~until21(s103)) | xuntil22(s103))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10826,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s103) | node20(s103) | (~until21(s103))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10825, 10824])).
% 1.71/1.67 tff(10827,plain,
% 1.71/1.67 (xuntil22(s103)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10826, 9422, 10820, 8550])).
% 1.71/1.67 tff(10828,plain,
% 1.71/1.67 (succ(s103, s104) <=> succ(s103, s104)),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10829,axiom,(succ(s103, s104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound104')).
% 1.71/1.67 tff(10830,plain,
% 1.71/1.67 (succ(s103, s104)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10829, 10828])).
% 1.71/1.67 tff(10831,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s103, s104)) | (~xuntil22(s103)) | until21(s104))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s103, s104)) | (~xuntil22(s103)) | until21(s104))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10832,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | ((~succ(s103, s104)) | (~xuntil22(s103)) | until21(s104))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10833,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil22(X)) | until21(Y))) | (~succ(s103, s104)) | (~xuntil22(s103)) | until21(s104)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10832, 10831])).
% 1.71/1.67 tff(10834,plain,
% 1.71/1.67 ((~xuntil22(s103)) | until21(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10833, 10830, 9440])).
% 1.71/1.67 tff(10835,plain,
% 1.71/1.67 (until21(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10834, 10827])).
% 1.71/1.67 tff(10836,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s104) | node20(s104) | (~until21(s104)))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s104) | node20(s104) | (~until21(s104)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10837,plain,
% 1.71/1.67 ((node20(s104) | (~until21(s104)) | xuntil22(s104)) <=> (xuntil22(s104) | node20(s104) | (~until21(s104)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10838,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s104) | (~until21(s104)) | xuntil22(s104))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (xuntil22(s104) | node20(s104) | (~until21(s104))))),
% 1.71/1.67 inference(monotonicity,[status(thm)],[10837])).
% 1.71/1.67 tff(10839,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s104) | (~until21(s104)) | xuntil22(s104))) <=> ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s104) | node20(s104) | (~until21(s104)))),
% 1.71/1.67 inference(transitivity,[status(thm)],[10838, 10836])).
% 1.71/1.67 tff(10840,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | (node20(s104) | (~until21(s104)) | xuntil22(s104))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10841,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | (~until21(X)) | xuntil22(X))) | xuntil22(s104) | node20(s104) | (~until21(s104))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10840, 10839])).
% 1.71/1.67 tff(10842,plain,
% 1.71/1.67 (xuntil22(s104) | node20(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10841, 9422, 10835])).
% 1.71/1.67 tff(10843,plain,
% 1.71/1.67 (xuntil22(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10842, 3447])).
% 1.71/1.67 tff(10844,plain,
% 1.71/1.67 (^[X: $i] : refl(((~last(X)) | (~xuntil2p24(X))) <=> ((~last(X)) | (~xuntil2p24(X))))),
% 1.71/1.67 inference(bind,[status(th)],[])).
% 1.71/1.67 tff(10845,plain,
% 1.71/1.67 (![X: $i] : ((~last(X)) | (~xuntil2p24(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(quant_intro,[status(thm)],[10844])).
% 1.71/1.67 tff(10846,plain,
% 1.71/1.67 (![X: $i] : ((~last(X)) | (~xuntil2p24(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10847,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty12')).
% 1.71/1.67 tff(10848,plain,
% 1.71/1.67 (![X: $i] : ((~last(X)) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10847, 10846])).
% 1.71/1.67 tff(10849,plain,(
% 1.71/1.67 ![X: $i] : ((~last(X)) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(skolemize,[status(sab)],[10848])).
% 1.71/1.67 tff(10850,plain,
% 1.71/1.67 (![X: $i] : ((~last(X)) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10849, 10845])).
% 1.71/1.67 tff(10851,plain,
% 1.71/1.67 (last(s104) <=> last(s104)),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10852,axiom,(last(s104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound105')).
% 1.71/1.67 tff(10853,plain,
% 1.71/1.67 (last(s104)),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10852, 10851])).
% 1.71/1.67 tff(10854,plain,
% 1.71/1.67 (((~![X: $i] : ((~last(X)) | (~xuntil2p24(X)))) | ((~last(s104)) | (~xuntil2p24(s104)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p24(X)))) | (~last(s104)) | (~xuntil2p24(s104)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10855,plain,
% 1.71/1.67 ((~![X: $i] : ((~last(X)) | (~xuntil2p24(X)))) | ((~last(s104)) | (~xuntil2p24(s104)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10856,plain,
% 1.71/1.67 ((~![X: $i] : ((~last(X)) | (~xuntil2p24(X)))) | (~last(s104)) | (~xuntil2p24(s104))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10855, 10854])).
% 1.71/1.67 tff(10857,plain,
% 1.71/1.67 (~xuntil2p24(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10856, 10853, 10850])).
% 1.71/1.67 tff(10858,plain,
% 1.71/1.67 (^[X: $i] : refl((node20(X) | xuntil2p24(X) | (~until2p23(X))) <=> (node20(X) | xuntil2p24(X) | (~until2p23(X))))),
% 1.71/1.67 inference(bind,[status(th)],[])).
% 1.71/1.67 tff(10859,plain,
% 1.71/1.67 (![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X))) <=> ![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(quant_intro,[status(thm)],[10858])).
% 1.71/1.67 tff(10860,plain,
% 1.71/1.67 (![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X))) <=> ![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10861,plain,
% 1.71/1.67 (^[X: $i] : rewrite(((node20(X) | xuntil2p24(X)) | (~until2p23(X))) <=> (node20(X) | xuntil2p24(X) | (~until2p23(X))))),
% 1.71/1.67 inference(bind,[status(th)],[])).
% 1.71/1.67 tff(10862,plain,
% 1.71/1.67 (![X: $i] : ((node20(X) | xuntil2p24(X)) | (~until2p23(X))) <=> ![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(quant_intro,[status(thm)],[10861])).
% 1.71/1.67 tff(10863,axiom,(![X: $i] : ((node20(X) | xuntil2p24(X)) | (~until2p23(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 1.71/1.67 tff(10864,plain,
% 1.71/1.67 (![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10863, 10862])).
% 1.71/1.67 tff(10865,plain,
% 1.71/1.67 (![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10864, 10860])).
% 1.71/1.67 tff(10866,plain,(
% 1.71/1.67 ![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(skolemize,[status(sab)],[10865])).
% 1.71/1.67 tff(10867,plain,
% 1.71/1.67 (![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10866, 10859])).
% 1.71/1.67 tff(10868,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s104) | xuntil2p24(s104) | (~until2p23(s104)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s104) | xuntil2p24(s104) | (~until2p23(s104)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10869,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s104) | xuntil2p24(s104) | (~until2p23(s104)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10870,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s104) | xuntil2p24(s104) | (~until2p23(s104))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10869, 10868])).
% 1.71/1.67 tff(10871,plain,
% 1.71/1.67 (node20(s104) | (~until2p23(s104))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10870, 10867, 10857])).
% 1.71/1.67 tff(10872,plain,
% 1.71/1.67 (~until2p23(s104)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10871, 3447])).
% 1.71/1.67 tff(10873,plain,
% 1.71/1.67 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X))) <=> ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X))))),
% 1.71/1.67 inference(bind,[status(th)],[])).
% 1.71/1.67 tff(10874,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(quant_intro,[status(thm)],[10873])).
% 1.71/1.67 tff(10875,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10876,plain,
% 1.71/1.67 (^[Y: $i, X: $i] : rewrite(((until2p23(Y) | (~succ(X, Y))) | (~xuntil2p24(X))) <=> ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X))))),
% 1.71/1.67 inference(bind,[status(th)],[])).
% 1.71/1.67 tff(10877,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((until2p23(Y) | (~succ(X, Y))) | (~xuntil2p24(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(quant_intro,[status(thm)],[10876])).
% 1.71/1.67 tff(10878,axiom,(![Y: $i, X: $i] : ((until2p23(Y) | (~succ(X, Y))) | (~xuntil2p24(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 1.71/1.67 tff(10879,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10878, 10877])).
% 1.71/1.67 tff(10880,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10879, 10875])).
% 1.71/1.67 tff(10881,plain,(
% 1.71/1.67 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(skolemize,[status(sab)],[10880])).
% 1.71/1.67 tff(10882,plain,
% 1.71/1.67 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10881, 10874])).
% 1.71/1.67 tff(10883,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s103, s104)) | until2p23(s104) | (~xuntil2p24(s103)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s103, s104)) | until2p23(s104) | (~xuntil2p24(s103)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10884,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s103, s104)) | until2p23(s104) | (~xuntil2p24(s103)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10885,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s103, s104)) | until2p23(s104) | (~xuntil2p24(s103))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10884, 10883])).
% 1.71/1.67 tff(10886,plain,
% 1.71/1.67 (until2p23(s104) | (~xuntil2p24(s103))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10885, 10830, 10882])).
% 1.71/1.67 tff(10887,plain,
% 1.71/1.67 (~xuntil2p24(s103)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10886, 10872])).
% 1.71/1.67 tff(10888,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s103) | xuntil2p24(s103) | (~until2p23(s103)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s103) | xuntil2p24(s103) | (~until2p23(s103)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10889,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s103) | xuntil2p24(s103) | (~until2p23(s103)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10890,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s103) | xuntil2p24(s103) | (~until2p23(s103))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10889, 10888])).
% 1.71/1.67 tff(10891,plain,
% 1.71/1.67 (xuntil2p24(s103) | (~until2p23(s103))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10890, 10867, 8550])).
% 1.71/1.67 tff(10892,plain,
% 1.71/1.67 (~until2p23(s103)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10891, 10887])).
% 1.71/1.67 tff(10893,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s102, s103)) | until2p23(s103) | (~xuntil2p24(s102)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s102, s103)) | until2p23(s103) | (~xuntil2p24(s102)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10894,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s102, s103)) | until2p23(s103) | (~xuntil2p24(s102)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10895,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s102, s103)) | until2p23(s103) | (~xuntil2p24(s102))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10894, 10893])).
% 1.71/1.67 tff(10896,plain,
% 1.71/1.67 (until2p23(s103) | (~xuntil2p24(s102))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10895, 8519, 10882])).
% 1.71/1.67 tff(10897,plain,
% 1.71/1.67 (~xuntil2p24(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10896, 10892])).
% 1.71/1.67 tff(10898,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s102) | xuntil2p24(s102) | (~until2p23(s102)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s102) | xuntil2p24(s102) | (~until2p23(s102)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10899,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s102) | xuntil2p24(s102) | (~until2p23(s102)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10900,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s102) | xuntil2p24(s102) | (~until2p23(s102))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10899, 10898])).
% 1.71/1.67 tff(10901,plain,
% 1.71/1.67 (xuntil2p24(s102) | (~until2p23(s102))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10900, 10867, 10807])).
% 1.71/1.67 tff(10902,plain,
% 1.71/1.67 (~until2p23(s102)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10901, 10897])).
% 1.71/1.67 tff(10903,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s101, s102)) | until2p23(s102) | (~xuntil2p24(s101)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s101, s102)) | until2p23(s102) | (~xuntil2p24(s101)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10904,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s101, s102)) | until2p23(s102) | (~xuntil2p24(s101)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10905,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s101, s102)) | until2p23(s102) | (~xuntil2p24(s101))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10904, 10903])).
% 1.71/1.67 tff(10906,plain,
% 1.71/1.67 (until2p23(s102) | (~xuntil2p24(s101))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10905, 8455, 10882])).
% 1.71/1.67 tff(10907,plain,
% 1.71/1.67 (~xuntil2p24(s101)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10906, 10902])).
% 1.71/1.67 tff(10908,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s101) | xuntil2p24(s101) | (~until2p23(s101)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s101) | xuntil2p24(s101) | (~until2p23(s101)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10909,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s101) | xuntil2p24(s101) | (~until2p23(s101)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10910,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s101) | xuntil2p24(s101) | (~until2p23(s101))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10909, 10908])).
% 1.71/1.67 tff(10911,plain,
% 1.71/1.67 (xuntil2p24(s101) | (~until2p23(s101))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10910, 10867, 8583])).
% 1.71/1.67 tff(10912,plain,
% 1.71/1.67 (~until2p23(s101)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10911, 10907])).
% 1.71/1.67 tff(10913,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s100, s101)) | until2p23(s101) | (~xuntil2p24(s100)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s100, s101)) | until2p23(s101) | (~xuntil2p24(s100)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10914,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s100, s101)) | until2p23(s101) | (~xuntil2p24(s100)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10915,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s100, s101)) | until2p23(s101) | (~xuntil2p24(s100))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10914, 10913])).
% 1.71/1.67 tff(10916,plain,
% 1.71/1.67 (until2p23(s101) | (~xuntil2p24(s100))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10915, 8360, 10882])).
% 1.71/1.67 tff(10917,plain,
% 1.71/1.67 (~xuntil2p24(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10916, 10912])).
% 1.71/1.67 tff(10918,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s100) | xuntil2p24(s100) | (~until2p23(s100)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s100) | xuntil2p24(s100) | (~until2p23(s100)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10919,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s100) | xuntil2p24(s100) | (~until2p23(s100)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10920,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s100) | xuntil2p24(s100) | (~until2p23(s100))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10919, 10918])).
% 1.71/1.67 tff(10921,plain,
% 1.71/1.67 (xuntil2p24(s100) | (~until2p23(s100))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10920, 10867, 8592])).
% 1.71/1.67 tff(10922,plain,
% 1.71/1.67 (~until2p23(s100)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10921, 10917])).
% 1.71/1.67 tff(10923,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s99, s100)) | until2p23(s100) | (~xuntil2p24(s99)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s99, s100)) | until2p23(s100) | (~xuntil2p24(s99)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10924,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s99, s100)) | until2p23(s100) | (~xuntil2p24(s99)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10925,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s99, s100)) | until2p23(s100) | (~xuntil2p24(s99))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10924, 10923])).
% 1.71/1.67 tff(10926,plain,
% 1.71/1.67 (until2p23(s100) | (~xuntil2p24(s99))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10925, 8299, 10882])).
% 1.71/1.67 tff(10927,plain,
% 1.71/1.67 (~xuntil2p24(s99)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10926, 10922])).
% 1.71/1.67 tff(10928,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s99) | xuntil2p24(s99) | (~until2p23(s99)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s99) | xuntil2p24(s99) | (~until2p23(s99)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10929,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s99) | xuntil2p24(s99) | (~until2p23(s99)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10930,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s99) | xuntil2p24(s99) | (~until2p23(s99))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10929, 10928])).
% 1.71/1.67 tff(10931,plain,
% 1.71/1.67 (xuntil2p24(s99) | (~until2p23(s99))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10930, 10867, 8600])).
% 1.71/1.67 tff(10932,plain,
% 1.71/1.67 (~until2p23(s99)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10931, 10927])).
% 1.71/1.67 tff(10933,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s98, s99)) | until2p23(s99) | (~xuntil2p24(s98)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s98, s99)) | until2p23(s99) | (~xuntil2p24(s98)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10934,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s98, s99)) | until2p23(s99) | (~xuntil2p24(s98)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10935,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s98, s99)) | until2p23(s99) | (~xuntil2p24(s98))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10934, 10933])).
% 1.71/1.67 tff(10936,plain,
% 1.71/1.67 (until2p23(s99) | (~xuntil2p24(s98))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10935, 8221, 10882])).
% 1.71/1.67 tff(10937,plain,
% 1.71/1.67 (~xuntil2p24(s98)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10936, 10932])).
% 1.71/1.67 tff(10938,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s98) | xuntil2p24(s98) | (~until2p23(s98)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s98) | xuntil2p24(s98) | (~until2p23(s98)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10939,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s98) | xuntil2p24(s98) | (~until2p23(s98)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10940,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s98) | xuntil2p24(s98) | (~until2p23(s98))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10939, 10938])).
% 1.71/1.67 tff(10941,plain,
% 1.71/1.67 (xuntil2p24(s98) | (~until2p23(s98))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10940, 10867, 10753])).
% 1.71/1.67 tff(10942,plain,
% 1.71/1.67 (~until2p23(s98)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10941, 10937])).
% 1.71/1.67 tff(10943,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s97, s98)) | until2p23(s98) | (~xuntil2p24(s97)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s97, s98)) | until2p23(s98) | (~xuntil2p24(s97)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10944,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s97, s98)) | until2p23(s98) | (~xuntil2p24(s97)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10945,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s97, s98)) | until2p23(s98) | (~xuntil2p24(s97))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10944, 10943])).
% 1.71/1.67 tff(10946,plain,
% 1.71/1.67 (until2p23(s98) | (~xuntil2p24(s97))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10945, 8122, 10882])).
% 1.71/1.67 tff(10947,plain,
% 1.71/1.67 (~xuntil2p24(s97)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10946, 10942])).
% 1.71/1.67 tff(10948,plain,
% 1.71/1.67 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s97) | xuntil2p24(s97) | (~until2p23(s97)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s97) | xuntil2p24(s97) | (~until2p23(s97)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10949,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s97) | xuntil2p24(s97) | (~until2p23(s97)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10950,plain,
% 1.71/1.67 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s97) | xuntil2p24(s97) | (~until2p23(s97))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10949, 10948])).
% 1.71/1.67 tff(10951,plain,
% 1.71/1.67 (xuntil2p24(s97) | (~until2p23(s97))),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10950, 10867, 8616])).
% 1.71/1.67 tff(10952,plain,
% 1.71/1.67 (~until2p23(s97)),
% 1.71/1.67 inference(unit_resolution,[status(thm)],[10951, 10947])).
% 1.71/1.67 tff(10953,plain,
% 1.71/1.67 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s96, s97)) | until2p23(s97) | (~xuntil2p24(s96)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s96, s97)) | until2p23(s97) | (~xuntil2p24(s96)))),
% 1.71/1.67 inference(rewrite,[status(thm)],[])).
% 1.71/1.67 tff(10954,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s96, s97)) | until2p23(s97) | (~xuntil2p24(s96)))),
% 1.71/1.67 inference(quant_inst,[status(thm)],[])).
% 1.71/1.67 tff(10955,plain,
% 1.71/1.67 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s96, s97)) | until2p23(s97) | (~xuntil2p24(s96))),
% 1.71/1.67 inference(modus_ponens,[status(thm)],[10954, 10953])).
% 1.71/1.67 tff(10956,plain,
% 1.71/1.67 (until2p23(s97) | (~xuntil2p24(s96))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10955, 8055, 10882])).
% 1.71/1.68 tff(10957,plain,
% 1.71/1.68 (~xuntil2p24(s96)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10956, 10952])).
% 1.71/1.68 tff(10958,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s96) | xuntil2p24(s96) | (~until2p23(s96)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s96) | xuntil2p24(s96) | (~until2p23(s96)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10959,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s96) | xuntil2p24(s96) | (~until2p23(s96)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10960,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s96) | xuntil2p24(s96) | (~until2p23(s96))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10959, 10958])).
% 1.71/1.68 tff(10961,plain,
% 1.71/1.68 (xuntil2p24(s96) | (~until2p23(s96))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10960, 10867, 8625])).
% 1.71/1.68 tff(10962,plain,
% 1.71/1.68 (~until2p23(s96)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10961, 10957])).
% 1.71/1.68 tff(10963,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s95, s96)) | until2p23(s96) | (~xuntil2p24(s95)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s95, s96)) | until2p23(s96) | (~xuntil2p24(s95)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10964,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s95, s96)) | until2p23(s96) | (~xuntil2p24(s95)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10965,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s95, s96)) | until2p23(s96) | (~xuntil2p24(s95))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10964, 10963])).
% 1.71/1.68 tff(10966,plain,
% 1.71/1.68 (until2p23(s96) | (~xuntil2p24(s95))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10965, 7966, 10882])).
% 1.71/1.68 tff(10967,plain,
% 1.71/1.68 (~xuntil2p24(s95)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10966, 10962])).
% 1.71/1.68 tff(10968,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s95) | xuntil2p24(s95) | (~until2p23(s95)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s95) | xuntil2p24(s95) | (~until2p23(s95)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10969,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s95) | xuntil2p24(s95) | (~until2p23(s95)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10970,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s95) | xuntil2p24(s95) | (~until2p23(s95))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10969, 10968])).
% 1.71/1.68 tff(10971,plain,
% 1.71/1.68 (xuntil2p24(s95) | (~until2p23(s95))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10970, 10867, 8633])).
% 1.71/1.68 tff(10972,plain,
% 1.71/1.68 (~until2p23(s95)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10971, 10967])).
% 1.71/1.68 tff(10973,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s94, s95)) | until2p23(s95) | (~xuntil2p24(s94)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s94, s95)) | until2p23(s95) | (~xuntil2p24(s94)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10974,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s94, s95)) | until2p23(s95) | (~xuntil2p24(s94)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10975,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s94, s95)) | until2p23(s95) | (~xuntil2p24(s94))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10974, 10973])).
% 1.71/1.68 tff(10976,plain,
% 1.71/1.68 (until2p23(s95) | (~xuntil2p24(s94))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10975, 7891, 10882])).
% 1.71/1.68 tff(10977,plain,
% 1.71/1.68 (~xuntil2p24(s94)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10976, 10972])).
% 1.71/1.68 tff(10978,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s94) | xuntil2p24(s94) | (~until2p23(s94)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s94) | xuntil2p24(s94) | (~until2p23(s94)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10979,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s94) | xuntil2p24(s94) | (~until2p23(s94)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10980,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s94) | xuntil2p24(s94) | (~until2p23(s94))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10979, 10978])).
% 1.71/1.68 tff(10981,plain,
% 1.71/1.68 (xuntil2p24(s94) | (~until2p23(s94))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10980, 10867, 10699])).
% 1.71/1.68 tff(10982,plain,
% 1.71/1.68 (~until2p23(s94)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10981, 10977])).
% 1.71/1.68 tff(10983,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s93, s94)) | until2p23(s94) | (~xuntil2p24(s93)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s93, s94)) | until2p23(s94) | (~xuntil2p24(s93)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10984,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s93, s94)) | until2p23(s94) | (~xuntil2p24(s93)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10985,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s93, s94)) | until2p23(s94) | (~xuntil2p24(s93))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10984, 10983])).
% 1.71/1.68 tff(10986,plain,
% 1.71/1.68 (until2p23(s94) | (~xuntil2p24(s93))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10985, 7827, 10882])).
% 1.71/1.68 tff(10987,plain,
% 1.71/1.68 (~xuntil2p24(s93)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10986, 10982])).
% 1.71/1.68 tff(10988,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s93) | xuntil2p24(s93) | (~until2p23(s93)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s93) | xuntil2p24(s93) | (~until2p23(s93)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10989,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s93) | xuntil2p24(s93) | (~until2p23(s93)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10990,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s93) | xuntil2p24(s93) | (~until2p23(s93))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10989, 10988])).
% 1.71/1.68 tff(10991,plain,
% 1.71/1.68 (xuntil2p24(s93) | (~until2p23(s93))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10990, 10867, 8649])).
% 1.71/1.68 tff(10992,plain,
% 1.71/1.68 (~until2p23(s93)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10991, 10987])).
% 1.71/1.68 tff(10993,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s92, s93)) | until2p23(s93) | (~xuntil2p24(s92)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s92, s93)) | until2p23(s93) | (~xuntil2p24(s92)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10994,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s92, s93)) | until2p23(s93) | (~xuntil2p24(s92)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(10995,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s92, s93)) | until2p23(s93) | (~xuntil2p24(s92))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10994, 10993])).
% 1.71/1.68 tff(10996,plain,
% 1.71/1.68 (until2p23(s93) | (~xuntil2p24(s92))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10995, 7732, 10882])).
% 1.71/1.68 tff(10997,plain,
% 1.71/1.68 (~xuntil2p24(s92)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[10996, 10992])).
% 1.71/1.68 tff(10998,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s92) | xuntil2p24(s92) | (~until2p23(s92)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s92) | xuntil2p24(s92) | (~until2p23(s92)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(10999,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s92) | xuntil2p24(s92) | (~until2p23(s92)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11000,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s92) | xuntil2p24(s92) | (~until2p23(s92))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[10999, 10998])).
% 1.71/1.68 tff(11001,plain,
% 1.71/1.68 (xuntil2p24(s92) | (~until2p23(s92))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11000, 10867, 8658])).
% 1.71/1.68 tff(11002,plain,
% 1.71/1.68 (~until2p23(s92)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11001, 10997])).
% 1.71/1.68 tff(11003,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s91, s92)) | until2p23(s92) | (~xuntil2p24(s91)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s91, s92)) | until2p23(s92) | (~xuntil2p24(s91)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11004,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s91, s92)) | until2p23(s92) | (~xuntil2p24(s91)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11005,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s91, s92)) | until2p23(s92) | (~xuntil2p24(s91))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11004, 11003])).
% 1.71/1.68 tff(11006,plain,
% 1.71/1.68 (until2p23(s92) | (~xuntil2p24(s91))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11005, 7671, 10882])).
% 1.71/1.68 tff(11007,plain,
% 1.71/1.68 (~xuntil2p24(s91)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11006, 11002])).
% 1.71/1.68 tff(11008,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s91) | xuntil2p24(s91) | (~until2p23(s91)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s91) | xuntil2p24(s91) | (~until2p23(s91)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11009,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s91) | xuntil2p24(s91) | (~until2p23(s91)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11010,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s91) | xuntil2p24(s91) | (~until2p23(s91))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11009, 11008])).
% 1.71/1.68 tff(11011,plain,
% 1.71/1.68 (xuntil2p24(s91) | (~until2p23(s91))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11010, 10867, 8666])).
% 1.71/1.68 tff(11012,plain,
% 1.71/1.68 (~until2p23(s91)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11011, 11007])).
% 1.71/1.68 tff(11013,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s90, s91)) | until2p23(s91) | (~xuntil2p24(s90)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s90, s91)) | until2p23(s91) | (~xuntil2p24(s90)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11014,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s90, s91)) | until2p23(s91) | (~xuntil2p24(s90)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11015,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s90, s91)) | until2p23(s91) | (~xuntil2p24(s90))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11014, 11013])).
% 1.71/1.68 tff(11016,plain,
% 1.71/1.68 (until2p23(s91) | (~xuntil2p24(s90))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11015, 7593, 10882])).
% 1.71/1.68 tff(11017,plain,
% 1.71/1.68 (~xuntil2p24(s90)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11016, 11012])).
% 1.71/1.68 tff(11018,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s90) | xuntil2p24(s90) | (~until2p23(s90)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s90) | xuntil2p24(s90) | (~until2p23(s90)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11019,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s90) | xuntil2p24(s90) | (~until2p23(s90)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11020,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s90) | xuntil2p24(s90) | (~until2p23(s90))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11019, 11018])).
% 1.71/1.68 tff(11021,plain,
% 1.71/1.68 (xuntil2p24(s90) | (~until2p23(s90))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11020, 10867, 10645])).
% 1.71/1.68 tff(11022,plain,
% 1.71/1.68 (~until2p23(s90)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11021, 11017])).
% 1.71/1.68 tff(11023,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s89, s90)) | until2p23(s90) | (~xuntil2p24(s89)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s89, s90)) | until2p23(s90) | (~xuntil2p24(s89)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11024,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s89, s90)) | until2p23(s90) | (~xuntil2p24(s89)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11025,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s89, s90)) | until2p23(s90) | (~xuntil2p24(s89))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11024, 11023])).
% 1.71/1.68 tff(11026,plain,
% 1.71/1.68 (until2p23(s90) | (~xuntil2p24(s89))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11025, 7494, 10882])).
% 1.71/1.68 tff(11027,plain,
% 1.71/1.68 (~xuntil2p24(s89)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11026, 11022])).
% 1.71/1.68 tff(11028,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s89) | xuntil2p24(s89) | (~until2p23(s89)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s89) | xuntil2p24(s89) | (~until2p23(s89)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11029,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s89) | xuntil2p24(s89) | (~until2p23(s89)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11030,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s89) | xuntil2p24(s89) | (~until2p23(s89))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11029, 11028])).
% 1.71/1.68 tff(11031,plain,
% 1.71/1.68 (xuntil2p24(s89) | (~until2p23(s89))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11030, 10867, 8682])).
% 1.71/1.68 tff(11032,plain,
% 1.71/1.68 (~until2p23(s89)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11031, 11027])).
% 1.71/1.68 tff(11033,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s88, s89)) | until2p23(s89) | (~xuntil2p24(s88)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s88, s89)) | until2p23(s89) | (~xuntil2p24(s88)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11034,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s88, s89)) | until2p23(s89) | (~xuntil2p24(s88)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11035,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s88, s89)) | until2p23(s89) | (~xuntil2p24(s88))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11034, 11033])).
% 1.71/1.68 tff(11036,plain,
% 1.71/1.68 (until2p23(s89) | (~xuntil2p24(s88))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11035, 7427, 10882])).
% 1.71/1.68 tff(11037,plain,
% 1.71/1.68 (~xuntil2p24(s88)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11036, 11032])).
% 1.71/1.68 tff(11038,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s88) | xuntil2p24(s88) | (~until2p23(s88)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s88) | xuntil2p24(s88) | (~until2p23(s88)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11039,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s88) | xuntil2p24(s88) | (~until2p23(s88)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11040,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s88) | xuntil2p24(s88) | (~until2p23(s88))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11039, 11038])).
% 1.71/1.68 tff(11041,plain,
% 1.71/1.68 (xuntil2p24(s88) | (~until2p23(s88))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11040, 10867, 8691])).
% 1.71/1.68 tff(11042,plain,
% 1.71/1.68 (~until2p23(s88)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11041, 11037])).
% 1.71/1.68 tff(11043,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s87, s88)) | until2p23(s88) | (~xuntil2p24(s87)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s87, s88)) | until2p23(s88) | (~xuntil2p24(s87)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11044,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s87, s88)) | until2p23(s88) | (~xuntil2p24(s87)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11045,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s87, s88)) | until2p23(s88) | (~xuntil2p24(s87))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11044, 11043])).
% 1.71/1.68 tff(11046,plain,
% 1.71/1.68 (until2p23(s88) | (~xuntil2p24(s87))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11045, 7338, 10882])).
% 1.71/1.68 tff(11047,plain,
% 1.71/1.68 (~xuntil2p24(s87)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11046, 11042])).
% 1.71/1.68 tff(11048,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s87) | xuntil2p24(s87) | (~until2p23(s87)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s87) | xuntil2p24(s87) | (~until2p23(s87)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11049,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s87) | xuntil2p24(s87) | (~until2p23(s87)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11050,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s87) | xuntil2p24(s87) | (~until2p23(s87))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11049, 11048])).
% 1.71/1.68 tff(11051,plain,
% 1.71/1.68 (xuntil2p24(s87) | (~until2p23(s87))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11050, 10867, 8699])).
% 1.71/1.68 tff(11052,plain,
% 1.71/1.68 (~until2p23(s87)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11051, 11047])).
% 1.71/1.68 tff(11053,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s86, s87)) | until2p23(s87) | (~xuntil2p24(s86)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s86, s87)) | until2p23(s87) | (~xuntil2p24(s86)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11054,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s86, s87)) | until2p23(s87) | (~xuntil2p24(s86)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11055,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s86, s87)) | until2p23(s87) | (~xuntil2p24(s86))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11054, 11053])).
% 1.71/1.68 tff(11056,plain,
% 1.71/1.68 (until2p23(s87) | (~xuntil2p24(s86))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11055, 7263, 10882])).
% 1.71/1.68 tff(11057,plain,
% 1.71/1.68 (~xuntil2p24(s86)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11056, 11052])).
% 1.71/1.68 tff(11058,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s86) | xuntil2p24(s86) | (~until2p23(s86)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s86) | xuntil2p24(s86) | (~until2p23(s86)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11059,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s86) | xuntil2p24(s86) | (~until2p23(s86)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11060,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s86) | xuntil2p24(s86) | (~until2p23(s86))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11059, 11058])).
% 1.71/1.68 tff(11061,plain,
% 1.71/1.68 (xuntil2p24(s86) | (~until2p23(s86))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11060, 10867, 10591])).
% 1.71/1.68 tff(11062,plain,
% 1.71/1.68 (~until2p23(s86)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11061, 11057])).
% 1.71/1.68 tff(11063,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s85, s86)) | until2p23(s86) | (~xuntil2p24(s85)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s85, s86)) | until2p23(s86) | (~xuntil2p24(s85)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11064,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s85, s86)) | until2p23(s86) | (~xuntil2p24(s85)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11065,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s85, s86)) | until2p23(s86) | (~xuntil2p24(s85))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11064, 11063])).
% 1.71/1.68 tff(11066,plain,
% 1.71/1.68 (until2p23(s86) | (~xuntil2p24(s85))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11065, 7199, 10882])).
% 1.71/1.68 tff(11067,plain,
% 1.71/1.68 (~xuntil2p24(s85)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11066, 11062])).
% 1.71/1.68 tff(11068,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s85) | xuntil2p24(s85) | (~until2p23(s85)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s85) | xuntil2p24(s85) | (~until2p23(s85)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11069,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s85) | xuntil2p24(s85) | (~until2p23(s85)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11070,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s85) | xuntil2p24(s85) | (~until2p23(s85))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11069, 11068])).
% 1.71/1.68 tff(11071,plain,
% 1.71/1.68 (xuntil2p24(s85) | (~until2p23(s85))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11070, 10867, 8715])).
% 1.71/1.68 tff(11072,plain,
% 1.71/1.68 (~until2p23(s85)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11071, 11067])).
% 1.71/1.68 tff(11073,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s84, s85)) | until2p23(s85) | (~xuntil2p24(s84)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s84, s85)) | until2p23(s85) | (~xuntil2p24(s84)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11074,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s84, s85)) | until2p23(s85) | (~xuntil2p24(s84)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11075,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s84, s85)) | until2p23(s85) | (~xuntil2p24(s84))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11074, 11073])).
% 1.71/1.68 tff(11076,plain,
% 1.71/1.68 (until2p23(s85) | (~xuntil2p24(s84))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11075, 7104, 10882])).
% 1.71/1.68 tff(11077,plain,
% 1.71/1.68 (~xuntil2p24(s84)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11076, 11072])).
% 1.71/1.68 tff(11078,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s84) | xuntil2p24(s84) | (~until2p23(s84)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s84) | xuntil2p24(s84) | (~until2p23(s84)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11079,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s84) | xuntil2p24(s84) | (~until2p23(s84)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11080,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s84) | xuntil2p24(s84) | (~until2p23(s84))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11079, 11078])).
% 1.71/1.68 tff(11081,plain,
% 1.71/1.68 (xuntil2p24(s84) | (~until2p23(s84))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11080, 10867, 8724])).
% 1.71/1.68 tff(11082,plain,
% 1.71/1.68 (~until2p23(s84)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11081, 11077])).
% 1.71/1.68 tff(11083,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s83, s84)) | until2p23(s84) | (~xuntil2p24(s83)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s83, s84)) | until2p23(s84) | (~xuntil2p24(s83)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11084,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s83, s84)) | until2p23(s84) | (~xuntil2p24(s83)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11085,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s83, s84)) | until2p23(s84) | (~xuntil2p24(s83))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11084, 11083])).
% 1.71/1.68 tff(11086,plain,
% 1.71/1.68 (until2p23(s84) | (~xuntil2p24(s83))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11085, 7043, 10882])).
% 1.71/1.68 tff(11087,plain,
% 1.71/1.68 (~xuntil2p24(s83)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11086, 11082])).
% 1.71/1.68 tff(11088,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s83) | xuntil2p24(s83) | (~until2p23(s83)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s83) | xuntil2p24(s83) | (~until2p23(s83)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11089,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s83) | xuntil2p24(s83) | (~until2p23(s83)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11090,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s83) | xuntil2p24(s83) | (~until2p23(s83))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11089, 11088])).
% 1.71/1.68 tff(11091,plain,
% 1.71/1.68 (xuntil2p24(s83) | (~until2p23(s83))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11090, 10867, 8732])).
% 1.71/1.68 tff(11092,plain,
% 1.71/1.68 (~until2p23(s83)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11091, 11087])).
% 1.71/1.68 tff(11093,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s82, s83)) | until2p23(s83) | (~xuntil2p24(s82)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s82, s83)) | until2p23(s83) | (~xuntil2p24(s82)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11094,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s82, s83)) | until2p23(s83) | (~xuntil2p24(s82)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11095,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s82, s83)) | until2p23(s83) | (~xuntil2p24(s82))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11094, 11093])).
% 1.71/1.68 tff(11096,plain,
% 1.71/1.68 (until2p23(s83) | (~xuntil2p24(s82))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11095, 6965, 10882])).
% 1.71/1.68 tff(11097,plain,
% 1.71/1.68 (~xuntil2p24(s82)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11096, 11092])).
% 1.71/1.68 tff(11098,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s82) | xuntil2p24(s82) | (~until2p23(s82)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s82) | xuntil2p24(s82) | (~until2p23(s82)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11099,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s82) | xuntil2p24(s82) | (~until2p23(s82)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11100,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s82) | xuntil2p24(s82) | (~until2p23(s82))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11099, 11098])).
% 1.71/1.68 tff(11101,plain,
% 1.71/1.68 (xuntil2p24(s82) | (~until2p23(s82))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11100, 10867, 10537])).
% 1.71/1.68 tff(11102,plain,
% 1.71/1.68 (~until2p23(s82)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11101, 11097])).
% 1.71/1.68 tff(11103,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s81, s82)) | until2p23(s82) | (~xuntil2p24(s81)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s81, s82)) | until2p23(s82) | (~xuntil2p24(s81)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11104,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s81, s82)) | until2p23(s82) | (~xuntil2p24(s81)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11105,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s81, s82)) | until2p23(s82) | (~xuntil2p24(s81))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11104, 11103])).
% 1.71/1.68 tff(11106,plain,
% 1.71/1.68 (until2p23(s82) | (~xuntil2p24(s81))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11105, 6866, 10882])).
% 1.71/1.68 tff(11107,plain,
% 1.71/1.68 (~xuntil2p24(s81)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11106, 11102])).
% 1.71/1.68 tff(11108,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s81) | xuntil2p24(s81) | (~until2p23(s81)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s81) | xuntil2p24(s81) | (~until2p23(s81)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11109,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s81) | xuntil2p24(s81) | (~until2p23(s81)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11110,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s81) | xuntil2p24(s81) | (~until2p23(s81))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11109, 11108])).
% 1.71/1.68 tff(11111,plain,
% 1.71/1.68 (xuntil2p24(s81) | (~until2p23(s81))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11110, 10867, 8748])).
% 1.71/1.68 tff(11112,plain,
% 1.71/1.68 (~until2p23(s81)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11111, 11107])).
% 1.71/1.68 tff(11113,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s80, s81)) | until2p23(s81) | (~xuntil2p24(s80)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s80, s81)) | until2p23(s81) | (~xuntil2p24(s80)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11114,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s80, s81)) | until2p23(s81) | (~xuntil2p24(s80)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11115,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s80, s81)) | until2p23(s81) | (~xuntil2p24(s80))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11114, 11113])).
% 1.71/1.68 tff(11116,plain,
% 1.71/1.68 (until2p23(s81) | (~xuntil2p24(s80))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11115, 6799, 10882])).
% 1.71/1.68 tff(11117,plain,
% 1.71/1.68 (~xuntil2p24(s80)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11116, 11112])).
% 1.71/1.68 tff(11118,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s80) | xuntil2p24(s80) | (~until2p23(s80)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s80) | xuntil2p24(s80) | (~until2p23(s80)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11119,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s80) | xuntil2p24(s80) | (~until2p23(s80)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11120,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s80) | xuntil2p24(s80) | (~until2p23(s80))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11119, 11118])).
% 1.71/1.68 tff(11121,plain,
% 1.71/1.68 (xuntil2p24(s80) | (~until2p23(s80))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11120, 10867, 8757])).
% 1.71/1.68 tff(11122,plain,
% 1.71/1.68 (~until2p23(s80)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11121, 11117])).
% 1.71/1.68 tff(11123,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s79, s80)) | until2p23(s80) | (~xuntil2p24(s79)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s79, s80)) | until2p23(s80) | (~xuntil2p24(s79)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11124,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s79, s80)) | until2p23(s80) | (~xuntil2p24(s79)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11125,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s79, s80)) | until2p23(s80) | (~xuntil2p24(s79))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11124, 11123])).
% 1.71/1.68 tff(11126,plain,
% 1.71/1.68 (until2p23(s80) | (~xuntil2p24(s79))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11125, 6710, 10882])).
% 1.71/1.68 tff(11127,plain,
% 1.71/1.68 (~xuntil2p24(s79)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11126, 11122])).
% 1.71/1.68 tff(11128,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s79) | xuntil2p24(s79) | (~until2p23(s79)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s79) | xuntil2p24(s79) | (~until2p23(s79)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11129,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s79) | xuntil2p24(s79) | (~until2p23(s79)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11130,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s79) | xuntil2p24(s79) | (~until2p23(s79))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11129, 11128])).
% 1.71/1.68 tff(11131,plain,
% 1.71/1.68 (xuntil2p24(s79) | (~until2p23(s79))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11130, 10867, 8765])).
% 1.71/1.68 tff(11132,plain,
% 1.71/1.68 (~until2p23(s79)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11131, 11127])).
% 1.71/1.68 tff(11133,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s78, s79)) | until2p23(s79) | (~xuntil2p24(s78)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s78, s79)) | until2p23(s79) | (~xuntil2p24(s78)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11134,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s78, s79)) | until2p23(s79) | (~xuntil2p24(s78)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11135,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s78, s79)) | until2p23(s79) | (~xuntil2p24(s78))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11134, 11133])).
% 1.71/1.68 tff(11136,plain,
% 1.71/1.68 (until2p23(s79) | (~xuntil2p24(s78))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11135, 6635, 10882])).
% 1.71/1.68 tff(11137,plain,
% 1.71/1.68 (~xuntil2p24(s78)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11136, 11132])).
% 1.71/1.68 tff(11138,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s78) | xuntil2p24(s78) | (~until2p23(s78)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s78) | xuntil2p24(s78) | (~until2p23(s78)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11139,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s78) | xuntil2p24(s78) | (~until2p23(s78)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11140,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s78) | xuntil2p24(s78) | (~until2p23(s78))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11139, 11138])).
% 1.71/1.68 tff(11141,plain,
% 1.71/1.68 (xuntil2p24(s78) | (~until2p23(s78))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11140, 10867, 10483])).
% 1.71/1.68 tff(11142,plain,
% 1.71/1.68 (~until2p23(s78)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11141, 11137])).
% 1.71/1.68 tff(11143,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s77, s78)) | until2p23(s78) | (~xuntil2p24(s77)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s77, s78)) | until2p23(s78) | (~xuntil2p24(s77)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11144,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s77, s78)) | until2p23(s78) | (~xuntil2p24(s77)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11145,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s77, s78)) | until2p23(s78) | (~xuntil2p24(s77))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11144, 11143])).
% 1.71/1.68 tff(11146,plain,
% 1.71/1.68 (until2p23(s78) | (~xuntil2p24(s77))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11145, 6571, 10882])).
% 1.71/1.68 tff(11147,plain,
% 1.71/1.68 (~xuntil2p24(s77)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11146, 11142])).
% 1.71/1.68 tff(11148,plain,
% 1.71/1.68 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s77) | xuntil2p24(s77) | (~until2p23(s77)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s77) | xuntil2p24(s77) | (~until2p23(s77)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11149,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s77) | xuntil2p24(s77) | (~until2p23(s77)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11150,plain,
% 1.71/1.68 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s77) | xuntil2p24(s77) | (~until2p23(s77))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11149, 11148])).
% 1.71/1.68 tff(11151,plain,
% 1.71/1.68 (xuntil2p24(s77) | (~until2p23(s77))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11150, 10867, 8781])).
% 1.71/1.68 tff(11152,plain,
% 1.71/1.68 (~until2p23(s77)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11151, 11147])).
% 1.71/1.68 tff(11153,plain,
% 1.71/1.68 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s76, s77)) | until2p23(s77) | (~xuntil2p24(s76)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s76, s77)) | until2p23(s77) | (~xuntil2p24(s76)))),
% 1.71/1.68 inference(rewrite,[status(thm)],[])).
% 1.71/1.68 tff(11154,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s76, s77)) | until2p23(s77) | (~xuntil2p24(s76)))),
% 1.71/1.68 inference(quant_inst,[status(thm)],[])).
% 1.71/1.68 tff(11155,plain,
% 1.71/1.68 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s76, s77)) | until2p23(s77) | (~xuntil2p24(s76))),
% 1.71/1.68 inference(modus_ponens,[status(thm)],[11154, 11153])).
% 1.71/1.68 tff(11156,plain,
% 1.71/1.68 (until2p23(s77) | (~xuntil2p24(s76))),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11155, 6476, 10882])).
% 1.71/1.68 tff(11157,plain,
% 1.71/1.68 (~xuntil2p24(s76)),
% 1.71/1.68 inference(unit_resolution,[status(thm)],[11156, 11152])).
% 1.71/1.69 tff(11158,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s76) | xuntil2p24(s76) | (~until2p23(s76)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s76) | xuntil2p24(s76) | (~until2p23(s76)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11159,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s76) | xuntil2p24(s76) | (~until2p23(s76)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11160,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s76) | xuntil2p24(s76) | (~until2p23(s76))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11159, 11158])).
% 1.71/1.69 tff(11161,plain,
% 1.71/1.69 (xuntil2p24(s76) | (~until2p23(s76))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11160, 10867, 8790])).
% 1.71/1.69 tff(11162,plain,
% 1.71/1.69 (~until2p23(s76)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11161, 11157])).
% 1.71/1.69 tff(11163,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s75, s76)) | until2p23(s76) | (~xuntil2p24(s75)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s75, s76)) | until2p23(s76) | (~xuntil2p24(s75)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11164,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s75, s76)) | until2p23(s76) | (~xuntil2p24(s75)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11165,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s75, s76)) | until2p23(s76) | (~xuntil2p24(s75))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11164, 11163])).
% 1.71/1.69 tff(11166,plain,
% 1.71/1.69 (until2p23(s76) | (~xuntil2p24(s75))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11165, 6415, 10882])).
% 1.71/1.69 tff(11167,plain,
% 1.71/1.69 (~xuntil2p24(s75)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11166, 11162])).
% 1.71/1.69 tff(11168,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s75) | xuntil2p24(s75) | (~until2p23(s75)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s75) | xuntil2p24(s75) | (~until2p23(s75)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11169,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s75) | xuntil2p24(s75) | (~until2p23(s75)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11170,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s75) | xuntil2p24(s75) | (~until2p23(s75))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11169, 11168])).
% 1.71/1.69 tff(11171,plain,
% 1.71/1.69 (xuntil2p24(s75) | (~until2p23(s75))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11170, 10867, 8798])).
% 1.71/1.69 tff(11172,plain,
% 1.71/1.69 (~until2p23(s75)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11171, 11167])).
% 1.71/1.69 tff(11173,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s74, s75)) | until2p23(s75) | (~xuntil2p24(s74)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s74, s75)) | until2p23(s75) | (~xuntil2p24(s74)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11174,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s74, s75)) | until2p23(s75) | (~xuntil2p24(s74)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11175,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s74, s75)) | until2p23(s75) | (~xuntil2p24(s74))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11174, 11173])).
% 1.71/1.69 tff(11176,plain,
% 1.71/1.69 (until2p23(s75) | (~xuntil2p24(s74))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11175, 6337, 10882])).
% 1.71/1.69 tff(11177,plain,
% 1.71/1.69 (~xuntil2p24(s74)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11176, 11172])).
% 1.71/1.69 tff(11178,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s74) | xuntil2p24(s74) | (~until2p23(s74)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s74) | xuntil2p24(s74) | (~until2p23(s74)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11179,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s74) | xuntil2p24(s74) | (~until2p23(s74)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11180,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s74) | xuntil2p24(s74) | (~until2p23(s74))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11179, 11178])).
% 1.71/1.69 tff(11181,plain,
% 1.71/1.69 (xuntil2p24(s74) | (~until2p23(s74))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11180, 10867, 10429])).
% 1.71/1.69 tff(11182,plain,
% 1.71/1.69 (~until2p23(s74)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11181, 11177])).
% 1.71/1.69 tff(11183,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s73, s74)) | until2p23(s74) | (~xuntil2p24(s73)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s73, s74)) | until2p23(s74) | (~xuntil2p24(s73)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11184,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s73, s74)) | until2p23(s74) | (~xuntil2p24(s73)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11185,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s73, s74)) | until2p23(s74) | (~xuntil2p24(s73))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11184, 11183])).
% 1.71/1.69 tff(11186,plain,
% 1.71/1.69 (until2p23(s74) | (~xuntil2p24(s73))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11185, 6238, 10882])).
% 1.71/1.69 tff(11187,plain,
% 1.71/1.69 (~xuntil2p24(s73)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11186, 11182])).
% 1.71/1.69 tff(11188,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s73) | xuntil2p24(s73) | (~until2p23(s73)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s73) | xuntil2p24(s73) | (~until2p23(s73)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11189,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s73) | xuntil2p24(s73) | (~until2p23(s73)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11190,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s73) | xuntil2p24(s73) | (~until2p23(s73))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11189, 11188])).
% 1.71/1.69 tff(11191,plain,
% 1.71/1.69 (xuntil2p24(s73) | (~until2p23(s73))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11190, 10867, 8814])).
% 1.71/1.69 tff(11192,plain,
% 1.71/1.69 (~until2p23(s73)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11191, 11187])).
% 1.71/1.69 tff(11193,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s72, s73)) | until2p23(s73) | (~xuntil2p24(s72)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s72, s73)) | until2p23(s73) | (~xuntil2p24(s72)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11194,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s72, s73)) | until2p23(s73) | (~xuntil2p24(s72)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11195,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s72, s73)) | until2p23(s73) | (~xuntil2p24(s72))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11194, 11193])).
% 1.71/1.69 tff(11196,plain,
% 1.71/1.69 (until2p23(s73) | (~xuntil2p24(s72))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11195, 6171, 10882])).
% 1.71/1.69 tff(11197,plain,
% 1.71/1.69 (~xuntil2p24(s72)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11196, 11192])).
% 1.71/1.69 tff(11198,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s72) | xuntil2p24(s72) | (~until2p23(s72)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s72) | xuntil2p24(s72) | (~until2p23(s72)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11199,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s72) | xuntil2p24(s72) | (~until2p23(s72)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11200,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s72) | xuntil2p24(s72) | (~until2p23(s72))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11199, 11198])).
% 1.71/1.69 tff(11201,plain,
% 1.71/1.69 (xuntil2p24(s72) | (~until2p23(s72))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11200, 10867, 8823])).
% 1.71/1.69 tff(11202,plain,
% 1.71/1.69 (~until2p23(s72)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11201, 11197])).
% 1.71/1.69 tff(11203,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s71, s72)) | until2p23(s72) | (~xuntil2p24(s71)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s71, s72)) | until2p23(s72) | (~xuntil2p24(s71)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11204,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s71, s72)) | until2p23(s72) | (~xuntil2p24(s71)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11205,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s71, s72)) | until2p23(s72) | (~xuntil2p24(s71))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11204, 11203])).
% 1.71/1.69 tff(11206,plain,
% 1.71/1.69 (until2p23(s72) | (~xuntil2p24(s71))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11205, 6082, 10882])).
% 1.71/1.69 tff(11207,plain,
% 1.71/1.69 (~xuntil2p24(s71)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11206, 11202])).
% 1.71/1.69 tff(11208,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s71) | xuntil2p24(s71) | (~until2p23(s71)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s71) | xuntil2p24(s71) | (~until2p23(s71)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11209,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s71) | xuntil2p24(s71) | (~until2p23(s71)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11210,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s71) | xuntil2p24(s71) | (~until2p23(s71))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11209, 11208])).
% 1.71/1.69 tff(11211,plain,
% 1.71/1.69 (xuntil2p24(s71) | (~until2p23(s71))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11210, 10867, 8831])).
% 1.71/1.69 tff(11212,plain,
% 1.71/1.69 (~until2p23(s71)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11211, 11207])).
% 1.71/1.69 tff(11213,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s70, s71)) | until2p23(s71) | (~xuntil2p24(s70)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s70, s71)) | until2p23(s71) | (~xuntil2p24(s70)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11214,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s70, s71)) | until2p23(s71) | (~xuntil2p24(s70)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11215,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s70, s71)) | until2p23(s71) | (~xuntil2p24(s70))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11214, 11213])).
% 1.71/1.69 tff(11216,plain,
% 1.71/1.69 (until2p23(s71) | (~xuntil2p24(s70))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11215, 6007, 10882])).
% 1.71/1.69 tff(11217,plain,
% 1.71/1.69 (~xuntil2p24(s70)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11216, 11212])).
% 1.71/1.69 tff(11218,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s70) | xuntil2p24(s70) | (~until2p23(s70)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s70) | xuntil2p24(s70) | (~until2p23(s70)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11219,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s70) | xuntil2p24(s70) | (~until2p23(s70)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11220,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s70) | xuntil2p24(s70) | (~until2p23(s70))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11219, 11218])).
% 1.71/1.69 tff(11221,plain,
% 1.71/1.69 (xuntil2p24(s70) | (~until2p23(s70))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11220, 10867, 10375])).
% 1.71/1.69 tff(11222,plain,
% 1.71/1.69 (~until2p23(s70)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11221, 11217])).
% 1.71/1.69 tff(11223,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s69, s70)) | until2p23(s70) | (~xuntil2p24(s69)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s69, s70)) | until2p23(s70) | (~xuntil2p24(s69)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11224,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s69, s70)) | until2p23(s70) | (~xuntil2p24(s69)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11225,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s69, s70)) | until2p23(s70) | (~xuntil2p24(s69))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11224, 11223])).
% 1.71/1.69 tff(11226,plain,
% 1.71/1.69 (until2p23(s70) | (~xuntil2p24(s69))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11225, 5943, 10882])).
% 1.71/1.69 tff(11227,plain,
% 1.71/1.69 (~xuntil2p24(s69)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11226, 11222])).
% 1.71/1.69 tff(11228,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s69) | xuntil2p24(s69) | (~until2p23(s69)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s69) | xuntil2p24(s69) | (~until2p23(s69)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11229,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s69) | xuntil2p24(s69) | (~until2p23(s69)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11230,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s69) | xuntil2p24(s69) | (~until2p23(s69))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11229, 11228])).
% 1.71/1.69 tff(11231,plain,
% 1.71/1.69 (xuntil2p24(s69) | (~until2p23(s69))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11230, 10867, 8847])).
% 1.71/1.69 tff(11232,plain,
% 1.71/1.69 (~until2p23(s69)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11231, 11227])).
% 1.71/1.69 tff(11233,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s68, s69)) | until2p23(s69) | (~xuntil2p24(s68)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s68, s69)) | until2p23(s69) | (~xuntil2p24(s68)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11234,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s68, s69)) | until2p23(s69) | (~xuntil2p24(s68)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11235,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s68, s69)) | until2p23(s69) | (~xuntil2p24(s68))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11234, 11233])).
% 1.71/1.69 tff(11236,plain,
% 1.71/1.69 (until2p23(s69) | (~xuntil2p24(s68))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11235, 5848, 10882])).
% 1.71/1.69 tff(11237,plain,
% 1.71/1.69 (~xuntil2p24(s68)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11236, 11232])).
% 1.71/1.69 tff(11238,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s68) | xuntil2p24(s68) | (~until2p23(s68)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s68) | xuntil2p24(s68) | (~until2p23(s68)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11239,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s68) | xuntil2p24(s68) | (~until2p23(s68)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11240,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s68) | xuntil2p24(s68) | (~until2p23(s68))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11239, 11238])).
% 1.71/1.69 tff(11241,plain,
% 1.71/1.69 (xuntil2p24(s68) | (~until2p23(s68))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11240, 10867, 8856])).
% 1.71/1.69 tff(11242,plain,
% 1.71/1.69 (~until2p23(s68)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11241, 11237])).
% 1.71/1.69 tff(11243,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s67, s68)) | until2p23(s68) | (~xuntil2p24(s67)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s67, s68)) | until2p23(s68) | (~xuntil2p24(s67)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11244,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s67, s68)) | until2p23(s68) | (~xuntil2p24(s67)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11245,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s67, s68)) | until2p23(s68) | (~xuntil2p24(s67))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11244, 11243])).
% 1.71/1.69 tff(11246,plain,
% 1.71/1.69 (until2p23(s68) | (~xuntil2p24(s67))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11245, 5787, 10882])).
% 1.71/1.69 tff(11247,plain,
% 1.71/1.69 (~xuntil2p24(s67)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11246, 11242])).
% 1.71/1.69 tff(11248,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s67) | xuntil2p24(s67) | (~until2p23(s67)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s67) | xuntil2p24(s67) | (~until2p23(s67)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11249,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s67) | xuntil2p24(s67) | (~until2p23(s67)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11250,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s67) | xuntil2p24(s67) | (~until2p23(s67))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11249, 11248])).
% 1.71/1.69 tff(11251,plain,
% 1.71/1.69 (xuntil2p24(s67) | (~until2p23(s67))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11250, 10867, 8864])).
% 1.71/1.69 tff(11252,plain,
% 1.71/1.69 (~until2p23(s67)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11251, 11247])).
% 1.71/1.69 tff(11253,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s66, s67)) | until2p23(s67) | (~xuntil2p24(s66)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s66, s67)) | until2p23(s67) | (~xuntil2p24(s66)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11254,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s66, s67)) | until2p23(s67) | (~xuntil2p24(s66)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11255,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s66, s67)) | until2p23(s67) | (~xuntil2p24(s66))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11254, 11253])).
% 1.71/1.69 tff(11256,plain,
% 1.71/1.69 (until2p23(s67) | (~xuntil2p24(s66))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11255, 5709, 10882])).
% 1.71/1.69 tff(11257,plain,
% 1.71/1.69 (~xuntil2p24(s66)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11256, 11252])).
% 1.71/1.69 tff(11258,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s66) | xuntil2p24(s66) | (~until2p23(s66)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s66) | xuntil2p24(s66) | (~until2p23(s66)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11259,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s66) | xuntil2p24(s66) | (~until2p23(s66)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11260,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s66) | xuntil2p24(s66) | (~until2p23(s66))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11259, 11258])).
% 1.71/1.69 tff(11261,plain,
% 1.71/1.69 (xuntil2p24(s66) | (~until2p23(s66))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11260, 10867, 10321])).
% 1.71/1.69 tff(11262,plain,
% 1.71/1.69 (~until2p23(s66)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11261, 11257])).
% 1.71/1.69 tff(11263,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s65, s66)) | until2p23(s66) | (~xuntil2p24(s65)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s65, s66)) | until2p23(s66) | (~xuntil2p24(s65)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11264,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s65, s66)) | until2p23(s66) | (~xuntil2p24(s65)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11265,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s65, s66)) | until2p23(s66) | (~xuntil2p24(s65))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11264, 11263])).
% 1.71/1.69 tff(11266,plain,
% 1.71/1.69 (until2p23(s66) | (~xuntil2p24(s65))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11265, 5610, 10882])).
% 1.71/1.69 tff(11267,plain,
% 1.71/1.69 (~xuntil2p24(s65)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11266, 11262])).
% 1.71/1.69 tff(11268,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s65) | xuntil2p24(s65) | (~until2p23(s65)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s65) | xuntil2p24(s65) | (~until2p23(s65)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11269,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s65) | xuntil2p24(s65) | (~until2p23(s65)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11270,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s65) | xuntil2p24(s65) | (~until2p23(s65))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11269, 11268])).
% 1.71/1.69 tff(11271,plain,
% 1.71/1.69 (xuntil2p24(s65) | (~until2p23(s65))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11270, 10867, 8880])).
% 1.71/1.69 tff(11272,plain,
% 1.71/1.69 (~until2p23(s65)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11271, 11267])).
% 1.71/1.69 tff(11273,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s64, s65)) | until2p23(s65) | (~xuntil2p24(s64)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s64, s65)) | until2p23(s65) | (~xuntil2p24(s64)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11274,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s64, s65)) | until2p23(s65) | (~xuntil2p24(s64)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11275,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s64, s65)) | until2p23(s65) | (~xuntil2p24(s64))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11274, 11273])).
% 1.71/1.69 tff(11276,plain,
% 1.71/1.69 (until2p23(s65) | (~xuntil2p24(s64))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11275, 5543, 10882])).
% 1.71/1.69 tff(11277,plain,
% 1.71/1.69 (~xuntil2p24(s64)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11276, 11272])).
% 1.71/1.69 tff(11278,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s64) | xuntil2p24(s64) | (~until2p23(s64)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s64) | xuntil2p24(s64) | (~until2p23(s64)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11279,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s64) | xuntil2p24(s64) | (~until2p23(s64)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11280,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s64) | xuntil2p24(s64) | (~until2p23(s64))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11279, 11278])).
% 1.71/1.69 tff(11281,plain,
% 1.71/1.69 (xuntil2p24(s64) | (~until2p23(s64))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11280, 10867, 8889])).
% 1.71/1.69 tff(11282,plain,
% 1.71/1.69 (~until2p23(s64)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11281, 11277])).
% 1.71/1.69 tff(11283,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s63, s64)) | until2p23(s64) | (~xuntil2p24(s63)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s63, s64)) | until2p23(s64) | (~xuntil2p24(s63)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11284,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s63, s64)) | until2p23(s64) | (~xuntil2p24(s63)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11285,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s63, s64)) | until2p23(s64) | (~xuntil2p24(s63))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11284, 11283])).
% 1.71/1.69 tff(11286,plain,
% 1.71/1.69 (until2p23(s64) | (~xuntil2p24(s63))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11285, 5454, 10882])).
% 1.71/1.69 tff(11287,plain,
% 1.71/1.69 (~xuntil2p24(s63)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11286, 11282])).
% 1.71/1.69 tff(11288,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s63) | xuntil2p24(s63) | (~until2p23(s63)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s63) | xuntil2p24(s63) | (~until2p23(s63)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11289,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s63) | xuntil2p24(s63) | (~until2p23(s63)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11290,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s63) | xuntil2p24(s63) | (~until2p23(s63))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11289, 11288])).
% 1.71/1.69 tff(11291,plain,
% 1.71/1.69 (xuntil2p24(s63) | (~until2p23(s63))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11290, 10867, 8897])).
% 1.71/1.69 tff(11292,plain,
% 1.71/1.69 (~until2p23(s63)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11291, 11287])).
% 1.71/1.69 tff(11293,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s62, s63)) | until2p23(s63) | (~xuntil2p24(s62)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s62, s63)) | until2p23(s63) | (~xuntil2p24(s62)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11294,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s62, s63)) | until2p23(s63) | (~xuntil2p24(s62)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11295,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s62, s63)) | until2p23(s63) | (~xuntil2p24(s62))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11294, 11293])).
% 1.71/1.69 tff(11296,plain,
% 1.71/1.69 (until2p23(s63) | (~xuntil2p24(s62))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11295, 5379, 10882])).
% 1.71/1.69 tff(11297,plain,
% 1.71/1.69 (~xuntil2p24(s62)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11296, 11292])).
% 1.71/1.69 tff(11298,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s62) | xuntil2p24(s62) | (~until2p23(s62)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s62) | xuntil2p24(s62) | (~until2p23(s62)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11299,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s62) | xuntil2p24(s62) | (~until2p23(s62)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11300,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s62) | xuntil2p24(s62) | (~until2p23(s62))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11299, 11298])).
% 1.71/1.69 tff(11301,plain,
% 1.71/1.69 (xuntil2p24(s62) | (~until2p23(s62))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11300, 10867, 10267])).
% 1.71/1.69 tff(11302,plain,
% 1.71/1.69 (~until2p23(s62)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11301, 11297])).
% 1.71/1.69 tff(11303,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s61, s62)) | until2p23(s62) | (~xuntil2p24(s61)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s61, s62)) | until2p23(s62) | (~xuntil2p24(s61)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11304,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s61, s62)) | until2p23(s62) | (~xuntil2p24(s61)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11305,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s61, s62)) | until2p23(s62) | (~xuntil2p24(s61))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11304, 11303])).
% 1.71/1.69 tff(11306,plain,
% 1.71/1.69 (until2p23(s62) | (~xuntil2p24(s61))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11305, 5315, 10882])).
% 1.71/1.69 tff(11307,plain,
% 1.71/1.69 (~xuntil2p24(s61)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11306, 11302])).
% 1.71/1.69 tff(11308,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s61) | xuntil2p24(s61) | (~until2p23(s61)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s61) | xuntil2p24(s61) | (~until2p23(s61)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11309,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s61) | xuntil2p24(s61) | (~until2p23(s61)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11310,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s61) | xuntil2p24(s61) | (~until2p23(s61))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11309, 11308])).
% 1.71/1.69 tff(11311,plain,
% 1.71/1.69 (xuntil2p24(s61) | (~until2p23(s61))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11310, 10867, 8913])).
% 1.71/1.69 tff(11312,plain,
% 1.71/1.69 (~until2p23(s61)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11311, 11307])).
% 1.71/1.69 tff(11313,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s60, s61)) | until2p23(s61) | (~xuntil2p24(s60)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s60, s61)) | until2p23(s61) | (~xuntil2p24(s60)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11314,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s60, s61)) | until2p23(s61) | (~xuntil2p24(s60)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11315,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s60, s61)) | until2p23(s61) | (~xuntil2p24(s60))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11314, 11313])).
% 1.71/1.69 tff(11316,plain,
% 1.71/1.69 (until2p23(s61) | (~xuntil2p24(s60))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11315, 5220, 10882])).
% 1.71/1.69 tff(11317,plain,
% 1.71/1.69 (~xuntil2p24(s60)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11316, 11312])).
% 1.71/1.69 tff(11318,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s60) | xuntil2p24(s60) | (~until2p23(s60)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s60) | xuntil2p24(s60) | (~until2p23(s60)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11319,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s60) | xuntil2p24(s60) | (~until2p23(s60)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11320,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s60) | xuntil2p24(s60) | (~until2p23(s60))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11319, 11318])).
% 1.71/1.69 tff(11321,plain,
% 1.71/1.69 (xuntil2p24(s60) | (~until2p23(s60))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11320, 10867, 8922])).
% 1.71/1.69 tff(11322,plain,
% 1.71/1.69 (~until2p23(s60)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11321, 11317])).
% 1.71/1.69 tff(11323,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s59, s60)) | until2p23(s60) | (~xuntil2p24(s59)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s59, s60)) | until2p23(s60) | (~xuntil2p24(s59)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11324,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s59, s60)) | until2p23(s60) | (~xuntil2p24(s59)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11325,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s59, s60)) | until2p23(s60) | (~xuntil2p24(s59))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11324, 11323])).
% 1.71/1.69 tff(11326,plain,
% 1.71/1.69 (until2p23(s60) | (~xuntil2p24(s59))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11325, 5159, 10882])).
% 1.71/1.69 tff(11327,plain,
% 1.71/1.69 (~xuntil2p24(s59)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11326, 11322])).
% 1.71/1.69 tff(11328,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s59) | xuntil2p24(s59) | (~until2p23(s59)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s59) | xuntil2p24(s59) | (~until2p23(s59)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11329,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s59) | xuntil2p24(s59) | (~until2p23(s59)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11330,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s59) | xuntil2p24(s59) | (~until2p23(s59))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11329, 11328])).
% 1.71/1.69 tff(11331,plain,
% 1.71/1.69 (xuntil2p24(s59) | (~until2p23(s59))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11330, 10867, 8930])).
% 1.71/1.69 tff(11332,plain,
% 1.71/1.69 (~until2p23(s59)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11331, 11327])).
% 1.71/1.69 tff(11333,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s58, s59)) | until2p23(s59) | (~xuntil2p24(s58)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s58, s59)) | until2p23(s59) | (~xuntil2p24(s58)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11334,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s58, s59)) | until2p23(s59) | (~xuntil2p24(s58)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11335,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s58, s59)) | until2p23(s59) | (~xuntil2p24(s58))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11334, 11333])).
% 1.71/1.69 tff(11336,plain,
% 1.71/1.69 (until2p23(s59) | (~xuntil2p24(s58))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11335, 5081, 10882])).
% 1.71/1.69 tff(11337,plain,
% 1.71/1.69 (~xuntil2p24(s58)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11336, 11332])).
% 1.71/1.69 tff(11338,plain,
% 1.71/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s58) | xuntil2p24(s58) | (~until2p23(s58)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s58) | xuntil2p24(s58) | (~until2p23(s58)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11339,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s58) | xuntil2p24(s58) | (~until2p23(s58)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11340,plain,
% 1.71/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s58) | xuntil2p24(s58) | (~until2p23(s58))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11339, 11338])).
% 1.71/1.69 tff(11341,plain,
% 1.71/1.69 (xuntil2p24(s58) | (~until2p23(s58))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11340, 10867, 10213])).
% 1.71/1.69 tff(11342,plain,
% 1.71/1.69 (~until2p23(s58)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11341, 11337])).
% 1.71/1.69 tff(11343,plain,
% 1.71/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s57, s58)) | until2p23(s58) | (~xuntil2p24(s57)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s57, s58)) | until2p23(s58) | (~xuntil2p24(s57)))),
% 1.71/1.69 inference(rewrite,[status(thm)],[])).
% 1.71/1.69 tff(11344,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s57, s58)) | until2p23(s58) | (~xuntil2p24(s57)))),
% 1.71/1.69 inference(quant_inst,[status(thm)],[])).
% 1.71/1.69 tff(11345,plain,
% 1.71/1.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s57, s58)) | until2p23(s58) | (~xuntil2p24(s57))),
% 1.71/1.69 inference(modus_ponens,[status(thm)],[11344, 11343])).
% 1.71/1.69 tff(11346,plain,
% 1.71/1.69 (until2p23(s58) | (~xuntil2p24(s57))),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11345, 4982, 10882])).
% 1.71/1.69 tff(11347,plain,
% 1.71/1.69 (~xuntil2p24(s57)),
% 1.71/1.69 inference(unit_resolution,[status(thm)],[11346, 11342])).
% 1.78/1.69 tff(11348,plain,
% 1.78/1.69 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s57) | xuntil2p24(s57) | (~until2p23(s57)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s57) | xuntil2p24(s57) | (~until2p23(s57)))),
% 1.78/1.69 inference(rewrite,[status(thm)],[])).
% 1.78/1.69 tff(11349,plain,
% 1.78/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s57) | xuntil2p24(s57) | (~until2p23(s57)))),
% 1.78/1.69 inference(quant_inst,[status(thm)],[])).
% 1.78/1.69 tff(11350,plain,
% 1.78/1.69 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s57) | xuntil2p24(s57) | (~until2p23(s57))),
% 1.78/1.69 inference(modus_ponens,[status(thm)],[11349, 11348])).
% 1.78/1.69 tff(11351,plain,
% 1.78/1.69 (xuntil2p24(s57) | (~until2p23(s57))),
% 1.78/1.69 inference(unit_resolution,[status(thm)],[11350, 10867, 8946])).
% 1.78/1.69 tff(11352,plain,
% 1.78/1.69 (~until2p23(s57)),
% 1.78/1.69 inference(unit_resolution,[status(thm)],[11351, 11347])).
% 1.78/1.69 tff(11353,plain,
% 1.78/1.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s56, s57)) | until2p23(s57) | (~xuntil2p24(s56)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s56, s57)) | until2p23(s57) | (~xuntil2p24(s56)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11354,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s56, s57)) | until2p23(s57) | (~xuntil2p24(s56)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11355,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s56, s57)) | until2p23(s57) | (~xuntil2p24(s56))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11354, 11353])).
% 1.78/1.70 tff(11356,plain,
% 1.78/1.70 (until2p23(s57) | (~xuntil2p24(s56))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11355, 4915, 10882])).
% 1.78/1.70 tff(11357,plain,
% 1.78/1.70 (~xuntil2p24(s56)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11356, 11352])).
% 1.78/1.70 tff(11358,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s56) | xuntil2p24(s56) | (~until2p23(s56)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s56) | xuntil2p24(s56) | (~until2p23(s56)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11359,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s56) | xuntil2p24(s56) | (~until2p23(s56)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11360,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s56) | xuntil2p24(s56) | (~until2p23(s56))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11359, 11358])).
% 1.78/1.70 tff(11361,plain,
% 1.78/1.70 (xuntil2p24(s56) | (~until2p23(s56))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11360, 10867, 8955])).
% 1.78/1.70 tff(11362,plain,
% 1.78/1.70 (~until2p23(s56)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11361, 11357])).
% 1.78/1.70 tff(11363,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s55, s56)) | until2p23(s56) | (~xuntil2p24(s55)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s55, s56)) | until2p23(s56) | (~xuntil2p24(s55)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11364,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s55, s56)) | until2p23(s56) | (~xuntil2p24(s55)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11365,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s55, s56)) | until2p23(s56) | (~xuntil2p24(s55))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11364, 11363])).
% 1.78/1.70 tff(11366,plain,
% 1.78/1.70 (until2p23(s56) | (~xuntil2p24(s55))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11365, 4826, 10882])).
% 1.78/1.70 tff(11367,plain,
% 1.78/1.70 (~xuntil2p24(s55)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11366, 11362])).
% 1.78/1.70 tff(11368,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s55) | xuntil2p24(s55) | (~until2p23(s55)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s55) | xuntil2p24(s55) | (~until2p23(s55)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11369,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s55) | xuntil2p24(s55) | (~until2p23(s55)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11370,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s55) | xuntil2p24(s55) | (~until2p23(s55))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11369, 11368])).
% 1.78/1.70 tff(11371,plain,
% 1.78/1.70 (xuntil2p24(s55) | (~until2p23(s55))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11370, 10867, 8963])).
% 1.78/1.70 tff(11372,plain,
% 1.78/1.70 (~until2p23(s55)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11371, 11367])).
% 1.78/1.70 tff(11373,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s54, s55)) | until2p23(s55) | (~xuntil2p24(s54)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s54, s55)) | until2p23(s55) | (~xuntil2p24(s54)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11374,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s54, s55)) | until2p23(s55) | (~xuntil2p24(s54)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11375,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s54, s55)) | until2p23(s55) | (~xuntil2p24(s54))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11374, 11373])).
% 1.78/1.70 tff(11376,plain,
% 1.78/1.70 (until2p23(s55) | (~xuntil2p24(s54))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11375, 4751, 10882])).
% 1.78/1.70 tff(11377,plain,
% 1.78/1.70 (~xuntil2p24(s54)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11376, 11372])).
% 1.78/1.70 tff(11378,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s54) | xuntil2p24(s54) | (~until2p23(s54)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s54) | xuntil2p24(s54) | (~until2p23(s54)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11379,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s54) | xuntil2p24(s54) | (~until2p23(s54)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11380,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s54) | xuntil2p24(s54) | (~until2p23(s54))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11379, 11378])).
% 1.78/1.70 tff(11381,plain,
% 1.78/1.70 (xuntil2p24(s54) | (~until2p23(s54))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11380, 10867, 10159])).
% 1.78/1.70 tff(11382,plain,
% 1.78/1.70 (~until2p23(s54)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11381, 11377])).
% 1.78/1.70 tff(11383,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s53, s54)) | until2p23(s54) | (~xuntil2p24(s53)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s53, s54)) | until2p23(s54) | (~xuntil2p24(s53)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11384,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s53, s54)) | until2p23(s54) | (~xuntil2p24(s53)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11385,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s53, s54)) | until2p23(s54) | (~xuntil2p24(s53))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11384, 11383])).
% 1.78/1.70 tff(11386,plain,
% 1.78/1.70 (until2p23(s54) | (~xuntil2p24(s53))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11385, 4687, 10882])).
% 1.78/1.70 tff(11387,plain,
% 1.78/1.70 (~xuntil2p24(s53)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11386, 11382])).
% 1.78/1.70 tff(11388,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s53) | xuntil2p24(s53) | (~until2p23(s53)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s53) | xuntil2p24(s53) | (~until2p23(s53)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11389,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s53) | xuntil2p24(s53) | (~until2p23(s53)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11390,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s53) | xuntil2p24(s53) | (~until2p23(s53))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11389, 11388])).
% 1.78/1.70 tff(11391,plain,
% 1.78/1.70 (xuntil2p24(s53) | (~until2p23(s53))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11390, 10867, 8979])).
% 1.78/1.70 tff(11392,plain,
% 1.78/1.70 (~until2p23(s53)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11391, 11387])).
% 1.78/1.70 tff(11393,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s52, s53)) | until2p23(s53) | (~xuntil2p24(s52)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s52, s53)) | until2p23(s53) | (~xuntil2p24(s52)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11394,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s52, s53)) | until2p23(s53) | (~xuntil2p24(s52)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11395,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s52, s53)) | until2p23(s53) | (~xuntil2p24(s52))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11394, 11393])).
% 1.78/1.70 tff(11396,plain,
% 1.78/1.70 (until2p23(s53) | (~xuntil2p24(s52))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11395, 4592, 10882])).
% 1.78/1.70 tff(11397,plain,
% 1.78/1.70 (~xuntil2p24(s52)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11396, 11392])).
% 1.78/1.70 tff(11398,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s52) | xuntil2p24(s52) | (~until2p23(s52)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s52) | xuntil2p24(s52) | (~until2p23(s52)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11399,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s52) | xuntil2p24(s52) | (~until2p23(s52)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11400,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s52) | xuntil2p24(s52) | (~until2p23(s52))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11399, 11398])).
% 1.78/1.70 tff(11401,plain,
% 1.78/1.70 (xuntil2p24(s52) | (~until2p23(s52))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11400, 10867, 8988])).
% 1.78/1.70 tff(11402,plain,
% 1.78/1.70 (~until2p23(s52)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11401, 11397])).
% 1.78/1.70 tff(11403,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s51, s52)) | until2p23(s52) | (~xuntil2p24(s51)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s51, s52)) | until2p23(s52) | (~xuntil2p24(s51)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11404,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s51, s52)) | until2p23(s52) | (~xuntil2p24(s51)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11405,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s51, s52)) | until2p23(s52) | (~xuntil2p24(s51))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11404, 11403])).
% 1.78/1.70 tff(11406,plain,
% 1.78/1.70 (until2p23(s52) | (~xuntil2p24(s51))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11405, 4531, 10882])).
% 1.78/1.70 tff(11407,plain,
% 1.78/1.70 (~xuntil2p24(s51)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11406, 11402])).
% 1.78/1.70 tff(11408,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s51) | xuntil2p24(s51) | (~until2p23(s51)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s51) | xuntil2p24(s51) | (~until2p23(s51)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11409,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s51) | xuntil2p24(s51) | (~until2p23(s51)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11410,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s51) | xuntil2p24(s51) | (~until2p23(s51))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11409, 11408])).
% 1.78/1.70 tff(11411,plain,
% 1.78/1.70 (xuntil2p24(s51) | (~until2p23(s51))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11410, 10867, 8996])).
% 1.78/1.70 tff(11412,plain,
% 1.78/1.70 (~until2p23(s51)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11411, 11407])).
% 1.78/1.70 tff(11413,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s50, s51)) | until2p23(s51) | (~xuntil2p24(s50)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s50, s51)) | until2p23(s51) | (~xuntil2p24(s50)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11414,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s50, s51)) | until2p23(s51) | (~xuntil2p24(s50)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11415,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s50, s51)) | until2p23(s51) | (~xuntil2p24(s50))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11414, 11413])).
% 1.78/1.70 tff(11416,plain,
% 1.78/1.70 (until2p23(s51) | (~xuntil2p24(s50))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11415, 4453, 10882])).
% 1.78/1.70 tff(11417,plain,
% 1.78/1.70 (~xuntil2p24(s50)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11416, 11412])).
% 1.78/1.70 tff(11418,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s50) | xuntil2p24(s50) | (~until2p23(s50)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s50) | xuntil2p24(s50) | (~until2p23(s50)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11419,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s50) | xuntil2p24(s50) | (~until2p23(s50)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11420,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s50) | xuntil2p24(s50) | (~until2p23(s50))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11419, 11418])).
% 1.78/1.70 tff(11421,plain,
% 1.78/1.70 (xuntil2p24(s50) | (~until2p23(s50))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11420, 10867, 10105])).
% 1.78/1.70 tff(11422,plain,
% 1.78/1.70 (~until2p23(s50)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11421, 11417])).
% 1.78/1.70 tff(11423,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s49, s50)) | until2p23(s50) | (~xuntil2p24(s49)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s49, s50)) | until2p23(s50) | (~xuntil2p24(s49)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11424,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s49, s50)) | until2p23(s50) | (~xuntil2p24(s49)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11425,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s49, s50)) | until2p23(s50) | (~xuntil2p24(s49))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11424, 11423])).
% 1.78/1.70 tff(11426,plain,
% 1.78/1.70 (until2p23(s50) | (~xuntil2p24(s49))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11425, 4354, 10882])).
% 1.78/1.70 tff(11427,plain,
% 1.78/1.70 (~xuntil2p24(s49)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11426, 11422])).
% 1.78/1.70 tff(11428,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s49) | xuntil2p24(s49) | (~until2p23(s49)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s49) | xuntil2p24(s49) | (~until2p23(s49)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11429,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s49) | xuntil2p24(s49) | (~until2p23(s49)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11430,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s49) | xuntil2p24(s49) | (~until2p23(s49))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11429, 11428])).
% 1.78/1.70 tff(11431,plain,
% 1.78/1.70 (xuntil2p24(s49) | (~until2p23(s49))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11430, 10867, 9012])).
% 1.78/1.70 tff(11432,plain,
% 1.78/1.70 (~until2p23(s49)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11431, 11427])).
% 1.78/1.70 tff(11433,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s48, s49)) | until2p23(s49) | (~xuntil2p24(s48)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s48, s49)) | until2p23(s49) | (~xuntil2p24(s48)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11434,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s48, s49)) | until2p23(s49) | (~xuntil2p24(s48)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11435,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s48, s49)) | until2p23(s49) | (~xuntil2p24(s48))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11434, 11433])).
% 1.78/1.70 tff(11436,plain,
% 1.78/1.70 (until2p23(s49) | (~xuntil2p24(s48))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11435, 4287, 10882])).
% 1.78/1.70 tff(11437,plain,
% 1.78/1.70 (~xuntil2p24(s48)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11436, 11432])).
% 1.78/1.70 tff(11438,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s48) | xuntil2p24(s48) | (~until2p23(s48)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s48) | xuntil2p24(s48) | (~until2p23(s48)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11439,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s48) | xuntil2p24(s48) | (~until2p23(s48)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11440,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s48) | xuntil2p24(s48) | (~until2p23(s48))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11439, 11438])).
% 1.78/1.70 tff(11441,plain,
% 1.78/1.70 (xuntil2p24(s48) | (~until2p23(s48))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11440, 10867, 9021])).
% 1.78/1.70 tff(11442,plain,
% 1.78/1.70 (~until2p23(s48)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11441, 11437])).
% 1.78/1.70 tff(11443,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s47, s48)) | until2p23(s48) | (~xuntil2p24(s47)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s47, s48)) | until2p23(s48) | (~xuntil2p24(s47)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11444,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s47, s48)) | until2p23(s48) | (~xuntil2p24(s47)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11445,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s47, s48)) | until2p23(s48) | (~xuntil2p24(s47))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11444, 11443])).
% 1.78/1.70 tff(11446,plain,
% 1.78/1.70 (until2p23(s48) | (~xuntil2p24(s47))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11445, 4198, 10882])).
% 1.78/1.70 tff(11447,plain,
% 1.78/1.70 (~xuntil2p24(s47)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11446, 11442])).
% 1.78/1.70 tff(11448,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s47) | xuntil2p24(s47) | (~until2p23(s47)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s47) | xuntil2p24(s47) | (~until2p23(s47)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11449,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s47) | xuntil2p24(s47) | (~until2p23(s47)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11450,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s47) | xuntil2p24(s47) | (~until2p23(s47))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11449, 11448])).
% 1.78/1.70 tff(11451,plain,
% 1.78/1.70 (xuntil2p24(s47) | (~until2p23(s47))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11450, 10867, 9029])).
% 1.78/1.70 tff(11452,plain,
% 1.78/1.70 (~until2p23(s47)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11451, 11447])).
% 1.78/1.70 tff(11453,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s46, s47)) | until2p23(s47) | (~xuntil2p24(s46)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s46, s47)) | until2p23(s47) | (~xuntil2p24(s46)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11454,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s46, s47)) | until2p23(s47) | (~xuntil2p24(s46)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11455,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s46, s47)) | until2p23(s47) | (~xuntil2p24(s46))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11454, 11453])).
% 1.78/1.70 tff(11456,plain,
% 1.78/1.70 (until2p23(s47) | (~xuntil2p24(s46))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11455, 4123, 10882])).
% 1.78/1.70 tff(11457,plain,
% 1.78/1.70 (~xuntil2p24(s46)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11456, 11452])).
% 1.78/1.70 tff(11458,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s46) | xuntil2p24(s46) | (~until2p23(s46)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s46) | xuntil2p24(s46) | (~until2p23(s46)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11459,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s46) | xuntil2p24(s46) | (~until2p23(s46)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11460,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s46) | xuntil2p24(s46) | (~until2p23(s46))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11459, 11458])).
% 1.78/1.70 tff(11461,plain,
% 1.78/1.70 (xuntil2p24(s46) | (~until2p23(s46))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11460, 10867, 10051])).
% 1.78/1.70 tff(11462,plain,
% 1.78/1.70 (~until2p23(s46)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11461, 11457])).
% 1.78/1.70 tff(11463,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s45, s46)) | until2p23(s46) | (~xuntil2p24(s45)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s45, s46)) | until2p23(s46) | (~xuntil2p24(s45)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11464,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s45, s46)) | until2p23(s46) | (~xuntil2p24(s45)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11465,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s45, s46)) | until2p23(s46) | (~xuntil2p24(s45))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11464, 11463])).
% 1.78/1.70 tff(11466,plain,
% 1.78/1.70 (until2p23(s46) | (~xuntil2p24(s45))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11465, 4059, 10882])).
% 1.78/1.70 tff(11467,plain,
% 1.78/1.70 (~xuntil2p24(s45)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11466, 11462])).
% 1.78/1.70 tff(11468,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s45) | xuntil2p24(s45) | (~until2p23(s45)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s45) | xuntil2p24(s45) | (~until2p23(s45)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11469,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s45) | xuntil2p24(s45) | (~until2p23(s45)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11470,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s45) | xuntil2p24(s45) | (~until2p23(s45))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11469, 11468])).
% 1.78/1.70 tff(11471,plain,
% 1.78/1.70 (xuntil2p24(s45) | (~until2p23(s45))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11470, 10867, 9045])).
% 1.78/1.70 tff(11472,plain,
% 1.78/1.70 (~until2p23(s45)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11471, 11467])).
% 1.78/1.70 tff(11473,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s44, s45)) | until2p23(s45) | (~xuntil2p24(s44)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s44, s45)) | until2p23(s45) | (~xuntil2p24(s44)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11474,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s44, s45)) | until2p23(s45) | (~xuntil2p24(s44)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11475,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s44, s45)) | until2p23(s45) | (~xuntil2p24(s44))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11474, 11473])).
% 1.78/1.70 tff(11476,plain,
% 1.78/1.70 (until2p23(s45) | (~xuntil2p24(s44))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11475, 3964, 10882])).
% 1.78/1.70 tff(11477,plain,
% 1.78/1.70 (~xuntil2p24(s44)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11476, 11472])).
% 1.78/1.70 tff(11478,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s44) | xuntil2p24(s44) | (~until2p23(s44)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s44) | xuntil2p24(s44) | (~until2p23(s44)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11479,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s44) | xuntil2p24(s44) | (~until2p23(s44)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11480,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s44) | xuntil2p24(s44) | (~until2p23(s44))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11479, 11478])).
% 1.78/1.70 tff(11481,plain,
% 1.78/1.70 (xuntil2p24(s44) | (~until2p23(s44))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11480, 10867, 9054])).
% 1.78/1.70 tff(11482,plain,
% 1.78/1.70 (~until2p23(s44)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11481, 11477])).
% 1.78/1.70 tff(11483,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s43, s44)) | until2p23(s44) | (~xuntil2p24(s43)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s43, s44)) | until2p23(s44) | (~xuntil2p24(s43)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11484,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s43, s44)) | until2p23(s44) | (~xuntil2p24(s43)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11485,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s43, s44)) | until2p23(s44) | (~xuntil2p24(s43))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11484, 11483])).
% 1.78/1.70 tff(11486,plain,
% 1.78/1.70 (until2p23(s44) | (~xuntil2p24(s43))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11485, 3903, 10882])).
% 1.78/1.70 tff(11487,plain,
% 1.78/1.70 (~xuntil2p24(s43)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11486, 11482])).
% 1.78/1.70 tff(11488,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s43) | xuntil2p24(s43) | (~until2p23(s43)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s43) | xuntil2p24(s43) | (~until2p23(s43)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11489,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s43) | xuntil2p24(s43) | (~until2p23(s43)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11490,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s43) | xuntil2p24(s43) | (~until2p23(s43))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11489, 11488])).
% 1.78/1.70 tff(11491,plain,
% 1.78/1.70 (xuntil2p24(s43) | (~until2p23(s43))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11490, 10867, 9062])).
% 1.78/1.70 tff(11492,plain,
% 1.78/1.70 (~until2p23(s43)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11491, 11487])).
% 1.78/1.70 tff(11493,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s42, s43)) | until2p23(s43) | (~xuntil2p24(s42)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s42, s43)) | until2p23(s43) | (~xuntil2p24(s42)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11494,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s42, s43)) | until2p23(s43) | (~xuntil2p24(s42)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11495,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s42, s43)) | until2p23(s43) | (~xuntil2p24(s42))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11494, 11493])).
% 1.78/1.70 tff(11496,plain,
% 1.78/1.70 (until2p23(s43) | (~xuntil2p24(s42))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11495, 3825, 10882])).
% 1.78/1.70 tff(11497,plain,
% 1.78/1.70 (~xuntil2p24(s42)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11496, 11492])).
% 1.78/1.70 tff(11498,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s42) | xuntil2p24(s42) | (~until2p23(s42)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s42) | xuntil2p24(s42) | (~until2p23(s42)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11499,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s42) | xuntil2p24(s42) | (~until2p23(s42)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11500,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s42) | xuntil2p24(s42) | (~until2p23(s42))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11499, 11498])).
% 1.78/1.70 tff(11501,plain,
% 1.78/1.70 (xuntil2p24(s42) | (~until2p23(s42))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11500, 10867, 9997])).
% 1.78/1.70 tff(11502,plain,
% 1.78/1.70 (~until2p23(s42)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11501, 11497])).
% 1.78/1.70 tff(11503,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s41, s42)) | until2p23(s42) | (~xuntil2p24(s41)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s41, s42)) | until2p23(s42) | (~xuntil2p24(s41)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11504,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s41, s42)) | until2p23(s42) | (~xuntil2p24(s41)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11505,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s41, s42)) | until2p23(s42) | (~xuntil2p24(s41))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11504, 11503])).
% 1.78/1.70 tff(11506,plain,
% 1.78/1.70 (until2p23(s42) | (~xuntil2p24(s41))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11505, 3726, 10882])).
% 1.78/1.70 tff(11507,plain,
% 1.78/1.70 (~xuntil2p24(s41)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11506, 11502])).
% 1.78/1.70 tff(11508,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s41) | xuntil2p24(s41) | (~until2p23(s41)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s41) | xuntil2p24(s41) | (~until2p23(s41)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11509,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s41) | xuntil2p24(s41) | (~until2p23(s41)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11510,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s41) | xuntil2p24(s41) | (~until2p23(s41))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11509, 11508])).
% 1.78/1.70 tff(11511,plain,
% 1.78/1.70 (xuntil2p24(s41) | (~until2p23(s41))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11510, 10867, 9078])).
% 1.78/1.70 tff(11512,plain,
% 1.78/1.70 (~until2p23(s41)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11511, 11507])).
% 1.78/1.70 tff(11513,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s40, s41)) | until2p23(s41) | (~xuntil2p24(s40)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s40, s41)) | until2p23(s41) | (~xuntil2p24(s40)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11514,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s40, s41)) | until2p23(s41) | (~xuntil2p24(s40)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11515,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s40, s41)) | until2p23(s41) | (~xuntil2p24(s40))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11514, 11513])).
% 1.78/1.70 tff(11516,plain,
% 1.78/1.70 (until2p23(s41) | (~xuntil2p24(s40))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11515, 3659, 10882])).
% 1.78/1.70 tff(11517,plain,
% 1.78/1.70 (~xuntil2p24(s40)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11516, 11512])).
% 1.78/1.70 tff(11518,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s40) | xuntil2p24(s40) | (~until2p23(s40)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s40) | xuntil2p24(s40) | (~until2p23(s40)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11519,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s40) | xuntil2p24(s40) | (~until2p23(s40)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11520,plain,
% 1.78/1.70 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s40) | xuntil2p24(s40) | (~until2p23(s40))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11519, 11518])).
% 1.78/1.70 tff(11521,plain,
% 1.78/1.70 (xuntil2p24(s40) | (~until2p23(s40))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11520, 10867, 9087])).
% 1.78/1.70 tff(11522,plain,
% 1.78/1.70 (~until2p23(s40)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11521, 11517])).
% 1.78/1.70 tff(11523,plain,
% 1.78/1.70 (^[Y: $i, X: $i] : refl(((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y)) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y)))),
% 1.78/1.70 inference(bind,[status(th)],[])).
% 1.78/1.70 tff(11524,plain,
% 1.78/1.70 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(quant_intro,[status(thm)],[11523])).
% 1.78/1.70 tff(11525,plain,
% 1.78/1.70 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y)) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11526,plain,
% 1.78/1.70 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p23(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~trans(X, Y)) | (~last(X)) | until2p23(Y))), ((((until2p23(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil22(X))) <=> (((~trans(X, Y)) | (~last(X)) | until2p23(Y)) | (~xuntil22(X))))), rewrite((((~trans(X, Y)) | (~last(X)) | until2p23(Y)) | (~xuntil22(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))), ((((until2p23(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil22(X))) <=> ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))))),
% 1.78/1.70 inference(bind,[status(th)],[])).
% 1.78/1.70 tff(11527,plain,
% 1.78/1.70 (![Y: $i, X: $i] : (((until2p23(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil22(X))) <=> ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(quant_intro,[status(thm)],[11526])).
% 1.78/1.70 tff(11528,axiom,(![Y: $i, X: $i] : (((until2p23(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil22(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 1.78/1.70 tff(11529,plain,
% 1.78/1.70 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11528, 11527])).
% 1.78/1.70 tff(11530,plain,
% 1.78/1.70 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11529, 11525])).
% 1.78/1.70 tff(11531,plain,(
% 1.78/1.70 ![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(skolemize,[status(sab)],[11530])).
% 1.78/1.70 tff(11532,plain,
% 1.78/1.70 (![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11531, 11524])).
% 1.78/1.70 tff(11533,assumption,(xuntil22(s104)), introduced(assumption)).
% 1.78/1.70 tff(11534,assumption,(~until2p23(s91)), introduced(assumption)).
% 1.78/1.70 tff(11535,assumption,(trans(s104, s91)), introduced(assumption)).
% 1.78/1.70 tff(11536,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11537,plain,
% 1.78/1.70 (((~trans(s104, s91)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s91)) <=> (until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11538,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s91)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91))))),
% 1.78/1.70 inference(monotonicity,[status(thm)],[11537])).
% 1.78/1.70 tff(11539,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s91)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91)))),
% 1.78/1.70 inference(transitivity,[status(thm)],[11538, 11536])).
% 1.78/1.70 tff(11540,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s91)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s91))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11541,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s91) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s91))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11540, 11539])).
% 1.78/1.70 tff(11542,plain,
% 1.78/1.70 ($false),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11541, 10853, 11535, 11532, 11534, 11533])).
% 1.78/1.70 tff(11543,plain,((~trans(s104, s91)) | until2p23(s91) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.70 tff(11544,plain,
% 1.78/1.70 (~trans(s104, s91)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11543, 11012, 10843])).
% 1.78/1.70 tff(11545,plain,
% 1.78/1.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s39, s40)) | until2p23(s40) | (~xuntil2p24(s39)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s39, s40)) | until2p23(s40) | (~xuntil2p24(s39)))),
% 1.78/1.70 inference(rewrite,[status(thm)],[])).
% 1.78/1.70 tff(11546,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s39, s40)) | until2p23(s40) | (~xuntil2p24(s39)))),
% 1.78/1.70 inference(quant_inst,[status(thm)],[])).
% 1.78/1.70 tff(11547,plain,
% 1.78/1.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s39, s40)) | until2p23(s40) | (~xuntil2p24(s39))),
% 1.78/1.70 inference(modus_ponens,[status(thm)],[11546, 11545])).
% 1.78/1.70 tff(11548,plain,
% 1.78/1.70 (until2p23(s40) | (~xuntil2p24(s39))),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11547, 3570, 10882])).
% 1.78/1.70 tff(11549,plain,
% 1.78/1.70 (~xuntil2p24(s39)),
% 1.78/1.70 inference(unit_resolution,[status(thm)],[11548, 11522])).
% 1.78/1.70 tff(11550,plain,
% 1.78/1.70 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s39) | xuntil2p24(s39) | (~until2p23(s39)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s39) | xuntil2p24(s39) | (~until2p23(s39)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11551,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s39) | xuntil2p24(s39) | (~until2p23(s39)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11552,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s39) | xuntil2p24(s39) | (~until2p23(s39))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11551, 11550])).
% 1.78/1.71 tff(11553,plain,
% 1.78/1.71 (xuntil2p24(s39) | (~until2p23(s39))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11552, 10867, 9095])).
% 1.78/1.71 tff(11554,plain,
% 1.78/1.71 (~until2p23(s39)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11553, 11549])).
% 1.78/1.71 tff(11555,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s38, s39)) | until2p23(s39) | (~xuntil2p24(s38)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s38, s39)) | until2p23(s39) | (~xuntil2p24(s38)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11556,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s38, s39)) | until2p23(s39) | (~xuntil2p24(s38)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11557,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s38, s39)) | until2p23(s39) | (~xuntil2p24(s38))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11556, 11555])).
% 1.78/1.71 tff(11558,plain,
% 1.78/1.71 (until2p23(s39) | (~xuntil2p24(s38))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11557, 3495, 10882])).
% 1.78/1.71 tff(11559,plain,
% 1.78/1.71 (~xuntil2p24(s38)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11558, 11554])).
% 1.78/1.71 tff(11560,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s38) | xuntil2p24(s38) | (~until2p23(s38)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s38) | xuntil2p24(s38) | (~until2p23(s38)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11561,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s38) | xuntil2p24(s38) | (~until2p23(s38)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11562,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s38) | xuntil2p24(s38) | (~until2p23(s38))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11561, 11560])).
% 1.78/1.71 tff(11563,plain,
% 1.78/1.71 (xuntil2p24(s38) | (~until2p23(s38))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11562, 10867, 9943])).
% 1.78/1.71 tff(11564,plain,
% 1.78/1.71 (~until2p23(s38)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11563, 11559])).
% 1.78/1.71 tff(11565,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s37, s38)) | until2p23(s38) | (~xuntil2p24(s37)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s37, s38)) | until2p23(s38) | (~xuntil2p24(s37)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11566,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s37, s38)) | until2p23(s38) | (~xuntil2p24(s37)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11567,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s37, s38)) | until2p23(s38) | (~xuntil2p24(s37))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11566, 11565])).
% 1.78/1.71 tff(11568,plain,
% 1.78/1.71 (until2p23(s38) | (~xuntil2p24(s37))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11567, 3416, 10882])).
% 1.78/1.71 tff(11569,plain,
% 1.78/1.71 (~xuntil2p24(s37)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11568, 11564])).
% 1.78/1.71 tff(11570,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s37) | xuntil2p24(s37) | (~until2p23(s37)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s37) | xuntil2p24(s37) | (~until2p23(s37)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11571,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s37) | xuntil2p24(s37) | (~until2p23(s37)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11572,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s37) | xuntil2p24(s37) | (~until2p23(s37))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11571, 11570])).
% 1.78/1.71 tff(11573,plain,
% 1.78/1.71 (xuntil2p24(s37) | (~until2p23(s37))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11572, 10867, 9104])).
% 1.78/1.71 tff(11574,plain,
% 1.78/1.71 (~until2p23(s37)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11573, 11569])).
% 1.78/1.71 tff(11575,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s36, s37)) | until2p23(s37) | (~xuntil2p24(s36)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s36, s37)) | until2p23(s37) | (~xuntil2p24(s36)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11576,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s36, s37)) | until2p23(s37) | (~xuntil2p24(s36)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11577,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s36, s37)) | until2p23(s37) | (~xuntil2p24(s36))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11576, 11575])).
% 1.78/1.71 tff(11578,plain,
% 1.78/1.71 (until2p23(s37) | (~xuntil2p24(s36))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11577, 3321, 10882])).
% 1.78/1.71 tff(11579,plain,
% 1.78/1.71 (~xuntil2p24(s36)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11578, 11574])).
% 1.78/1.71 tff(11580,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s36) | xuntil2p24(s36) | (~until2p23(s36)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s36) | xuntil2p24(s36) | (~until2p23(s36)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11581,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s36) | xuntil2p24(s36) | (~until2p23(s36)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11582,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s36) | xuntil2p24(s36) | (~until2p23(s36))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11581, 11580])).
% 1.78/1.71 tff(11583,plain,
% 1.78/1.71 (xuntil2p24(s36) | (~until2p23(s36))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11582, 10867, 9113])).
% 1.78/1.71 tff(11584,plain,
% 1.78/1.71 (~until2p23(s36)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11583, 11579])).
% 1.78/1.71 tff(11585,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s35, s36)) | until2p23(s36) | (~xuntil2p24(s35)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s35, s36)) | until2p23(s36) | (~xuntil2p24(s35)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11586,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s35, s36)) | until2p23(s36) | (~xuntil2p24(s35)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11587,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s35, s36)) | until2p23(s36) | (~xuntil2p24(s35))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11586, 11585])).
% 1.78/1.71 tff(11588,plain,
% 1.78/1.71 (until2p23(s36) | (~xuntil2p24(s35))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11587, 3260, 10882])).
% 1.78/1.71 tff(11589,plain,
% 1.78/1.71 (~xuntil2p24(s35)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11588, 11584])).
% 1.78/1.71 tff(11590,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s35) | xuntil2p24(s35) | (~until2p23(s35)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s35) | xuntil2p24(s35) | (~until2p23(s35)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11591,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s35) | xuntil2p24(s35) | (~until2p23(s35)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11592,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s35) | xuntil2p24(s35) | (~until2p23(s35))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11591, 11590])).
% 1.78/1.71 tff(11593,plain,
% 1.78/1.71 (xuntil2p24(s35) | (~until2p23(s35))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11592, 10867, 9121])).
% 1.78/1.71 tff(11594,plain,
% 1.78/1.71 (~until2p23(s35)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11593, 11589])).
% 1.78/1.71 tff(11595,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s34, s35)) | until2p23(s35) | (~xuntil2p24(s34)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s34, s35)) | until2p23(s35) | (~xuntil2p24(s34)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11596,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s34, s35)) | until2p23(s35) | (~xuntil2p24(s34)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11597,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s34, s35)) | until2p23(s35) | (~xuntil2p24(s34))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11596, 11595])).
% 1.78/1.71 tff(11598,plain,
% 1.78/1.71 (until2p23(s35) | (~xuntil2p24(s34))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11597, 3182, 10882])).
% 1.78/1.71 tff(11599,plain,
% 1.78/1.71 (~xuntil2p24(s34)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11598, 11594])).
% 1.78/1.71 tff(11600,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s34) | xuntil2p24(s34) | (~until2p23(s34)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s34) | xuntil2p24(s34) | (~until2p23(s34)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11601,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s34) | xuntil2p24(s34) | (~until2p23(s34)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11602,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s34) | xuntil2p24(s34) | (~until2p23(s34))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11601, 11600])).
% 1.78/1.71 tff(11603,plain,
% 1.78/1.71 (xuntil2p24(s34) | (~until2p23(s34))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11602, 10867, 9889])).
% 1.78/1.71 tff(11604,plain,
% 1.78/1.71 (~until2p23(s34)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11603, 11599])).
% 1.78/1.71 tff(11605,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s33, s34)) | until2p23(s34) | (~xuntil2p24(s33)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s33, s34)) | until2p23(s34) | (~xuntil2p24(s33)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11606,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s33, s34)) | until2p23(s34) | (~xuntil2p24(s33)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11607,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s33, s34)) | until2p23(s34) | (~xuntil2p24(s33))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11606, 11605])).
% 1.78/1.71 tff(11608,plain,
% 1.78/1.71 (until2p23(s34) | (~xuntil2p24(s33))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11607, 3083, 10882])).
% 1.78/1.71 tff(11609,plain,
% 1.78/1.71 (~xuntil2p24(s33)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11608, 11604])).
% 1.78/1.71 tff(11610,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s33) | xuntil2p24(s33) | (~until2p23(s33)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s33) | xuntil2p24(s33) | (~until2p23(s33)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11611,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s33) | xuntil2p24(s33) | (~until2p23(s33)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11612,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s33) | xuntil2p24(s33) | (~until2p23(s33))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11611, 11610])).
% 1.78/1.71 tff(11613,plain,
% 1.78/1.71 (xuntil2p24(s33) | (~until2p23(s33))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11612, 10867, 9137])).
% 1.78/1.71 tff(11614,plain,
% 1.78/1.71 (~until2p23(s33)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11613, 11609])).
% 1.78/1.71 tff(11615,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s32, s33)) | until2p23(s33) | (~xuntil2p24(s32)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s32, s33)) | until2p23(s33) | (~xuntil2p24(s32)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11616,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s32, s33)) | until2p23(s33) | (~xuntil2p24(s32)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11617,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s32, s33)) | until2p23(s33) | (~xuntil2p24(s32))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11616, 11615])).
% 1.78/1.71 tff(11618,plain,
% 1.78/1.71 (until2p23(s33) | (~xuntil2p24(s32))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11617, 3016, 10882])).
% 1.78/1.71 tff(11619,plain,
% 1.78/1.71 (~xuntil2p24(s32)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11618, 11614])).
% 1.78/1.71 tff(11620,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s32) | xuntil2p24(s32) | (~until2p23(s32)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s32) | xuntil2p24(s32) | (~until2p23(s32)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11621,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s32) | xuntil2p24(s32) | (~until2p23(s32)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11622,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s32) | xuntil2p24(s32) | (~until2p23(s32))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11621, 11620])).
% 1.78/1.71 tff(11623,plain,
% 1.78/1.71 (xuntil2p24(s32) | (~until2p23(s32))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11622, 10867, 9146])).
% 1.78/1.71 tff(11624,plain,
% 1.78/1.71 (~until2p23(s32)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11623, 11619])).
% 1.78/1.71 tff(11625,assumption,(~until2p23(s32)), introduced(assumption)).
% 1.78/1.71 tff(11626,assumption,(trans(s104, s32)), introduced(assumption)).
% 1.78/1.71 tff(11627,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11628,plain,
% 1.78/1.71 (((~trans(s104, s32)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s32)) <=> (until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11629,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s32)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32))))),
% 1.78/1.71 inference(monotonicity,[status(thm)],[11628])).
% 1.78/1.71 tff(11630,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s32)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32)))),
% 1.78/1.71 inference(transitivity,[status(thm)],[11629, 11627])).
% 1.78/1.71 tff(11631,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s32)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s32))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11632,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s32) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s32))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11631, 11630])).
% 1.78/1.71 tff(11633,plain,
% 1.78/1.71 ($false),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11632, 10853, 11626, 11532, 11625, 11533])).
% 1.78/1.71 tff(11634,plain,((~trans(s104, s32)) | until2p23(s32) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.71 tff(11635,plain,
% 1.78/1.71 (~trans(s104, s32)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11634, 11624, 10843])).
% 1.78/1.71 tff(11636,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s31, s32)) | until2p23(s32) | (~xuntil2p24(s31)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s31, s32)) | until2p23(s32) | (~xuntil2p24(s31)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11637,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s31, s32)) | until2p23(s32) | (~xuntil2p24(s31)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11638,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s31, s32)) | until2p23(s32) | (~xuntil2p24(s31))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11637, 11636])).
% 1.78/1.71 tff(11639,plain,
% 1.78/1.71 (until2p23(s32) | (~xuntil2p24(s31))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11638, 2927, 10882])).
% 1.78/1.71 tff(11640,plain,
% 1.78/1.71 (~xuntil2p24(s31)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11639, 11624])).
% 1.78/1.71 tff(11641,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s31) | xuntil2p24(s31) | (~until2p23(s31)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s31) | xuntil2p24(s31) | (~until2p23(s31)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11642,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s31) | xuntil2p24(s31) | (~until2p23(s31)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11643,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s31) | xuntil2p24(s31) | (~until2p23(s31))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11642, 11641])).
% 1.78/1.71 tff(11644,plain,
% 1.78/1.71 (xuntil2p24(s31) | (~until2p23(s31))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11643, 10867, 9154])).
% 1.78/1.71 tff(11645,plain,
% 1.78/1.71 (~until2p23(s31)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11644, 11640])).
% 1.78/1.71 tff(11646,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s30, s31)) | until2p23(s31) | (~xuntil2p24(s30)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s30, s31)) | until2p23(s31) | (~xuntil2p24(s30)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11647,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s30, s31)) | until2p23(s31) | (~xuntil2p24(s30)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11648,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s30, s31)) | until2p23(s31) | (~xuntil2p24(s30))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11647, 11646])).
% 1.78/1.71 tff(11649,plain,
% 1.78/1.71 (until2p23(s31) | (~xuntil2p24(s30))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11648, 2852, 10882])).
% 1.78/1.71 tff(11650,plain,
% 1.78/1.71 (~xuntil2p24(s30)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11649, 11645])).
% 1.78/1.71 tff(11651,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s30) | xuntil2p24(s30) | (~until2p23(s30)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s30) | xuntil2p24(s30) | (~until2p23(s30)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11652,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s30) | xuntil2p24(s30) | (~until2p23(s30)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11653,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s30) | xuntil2p24(s30) | (~until2p23(s30))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11652, 11651])).
% 1.78/1.71 tff(11654,plain,
% 1.78/1.71 (xuntil2p24(s30) | (~until2p23(s30))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11653, 10867, 9835])).
% 1.78/1.71 tff(11655,plain,
% 1.78/1.71 (~until2p23(s30)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11654, 11650])).
% 1.78/1.71 tff(11656,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s29, s30)) | until2p23(s30) | (~xuntil2p24(s29)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s29, s30)) | until2p23(s30) | (~xuntil2p24(s29)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11657,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s29, s30)) | until2p23(s30) | (~xuntil2p24(s29)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11658,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s29, s30)) | until2p23(s30) | (~xuntil2p24(s29))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11657, 11656])).
% 1.78/1.71 tff(11659,plain,
% 1.78/1.71 (until2p23(s30) | (~xuntil2p24(s29))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11658, 2788, 10882])).
% 1.78/1.71 tff(11660,plain,
% 1.78/1.71 (~xuntil2p24(s29)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11659, 11655])).
% 1.78/1.71 tff(11661,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s29) | xuntil2p24(s29) | (~until2p23(s29)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s29) | xuntil2p24(s29) | (~until2p23(s29)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11662,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s29) | xuntil2p24(s29) | (~until2p23(s29)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11663,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s29) | xuntil2p24(s29) | (~until2p23(s29))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11662, 11661])).
% 1.78/1.71 tff(11664,plain,
% 1.78/1.71 (xuntil2p24(s29) | (~until2p23(s29))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11663, 10867, 9170])).
% 1.78/1.71 tff(11665,plain,
% 1.78/1.71 (~until2p23(s29)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11664, 11660])).
% 1.78/1.71 tff(11666,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s28, s29)) | until2p23(s29) | (~xuntil2p24(s28)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s28, s29)) | until2p23(s29) | (~xuntil2p24(s28)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11667,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s28, s29)) | until2p23(s29) | (~xuntil2p24(s28)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11668,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s28, s29)) | until2p23(s29) | (~xuntil2p24(s28))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11667, 11666])).
% 1.78/1.71 tff(11669,plain,
% 1.78/1.71 (until2p23(s29) | (~xuntil2p24(s28))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11668, 2693, 10882])).
% 1.78/1.71 tff(11670,plain,
% 1.78/1.71 (~xuntil2p24(s28)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11669, 11665])).
% 1.78/1.71 tff(11671,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s28) | xuntil2p24(s28) | (~until2p23(s28)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s28) | xuntil2p24(s28) | (~until2p23(s28)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11672,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s28) | xuntil2p24(s28) | (~until2p23(s28)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11673,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s28) | xuntil2p24(s28) | (~until2p23(s28))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11672, 11671])).
% 1.78/1.71 tff(11674,plain,
% 1.78/1.71 (xuntil2p24(s28) | (~until2p23(s28))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11673, 10867, 9179])).
% 1.78/1.71 tff(11675,plain,
% 1.78/1.71 (~until2p23(s28)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11674, 11670])).
% 1.78/1.71 tff(11676,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s27, s28)) | until2p23(s28) | (~xuntil2p24(s27)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s27, s28)) | until2p23(s28) | (~xuntil2p24(s27)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11677,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s27, s28)) | until2p23(s28) | (~xuntil2p24(s27)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11678,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s27, s28)) | until2p23(s28) | (~xuntil2p24(s27))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11677, 11676])).
% 1.78/1.71 tff(11679,plain,
% 1.78/1.71 (until2p23(s28) | (~xuntil2p24(s27))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11678, 2632, 10882])).
% 1.78/1.71 tff(11680,plain,
% 1.78/1.71 (~xuntil2p24(s27)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11679, 11675])).
% 1.78/1.71 tff(11681,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s27) | xuntil2p24(s27) | (~until2p23(s27)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s27) | xuntil2p24(s27) | (~until2p23(s27)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11682,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s27) | xuntil2p24(s27) | (~until2p23(s27)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11683,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s27) | xuntil2p24(s27) | (~until2p23(s27))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11682, 11681])).
% 1.78/1.71 tff(11684,plain,
% 1.78/1.71 (xuntil2p24(s27) | (~until2p23(s27))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11683, 10867, 9187])).
% 1.78/1.71 tff(11685,plain,
% 1.78/1.71 (~until2p23(s27)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11684, 11680])).
% 1.78/1.71 tff(11686,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s26, s27)) | until2p23(s27) | (~xuntil2p24(s26)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s26, s27)) | until2p23(s27) | (~xuntil2p24(s26)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11687,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s26, s27)) | until2p23(s27) | (~xuntil2p24(s26)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11688,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s26, s27)) | until2p23(s27) | (~xuntil2p24(s26))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11687, 11686])).
% 1.78/1.71 tff(11689,plain,
% 1.78/1.71 (until2p23(s27) | (~xuntil2p24(s26))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11688, 2554, 10882])).
% 1.78/1.71 tff(11690,plain,
% 1.78/1.71 (~xuntil2p24(s26)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11689, 11685])).
% 1.78/1.71 tff(11691,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s26) | xuntil2p24(s26) | (~until2p23(s26)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s26) | xuntil2p24(s26) | (~until2p23(s26)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11692,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s26) | xuntil2p24(s26) | (~until2p23(s26)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11693,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s26) | xuntil2p24(s26) | (~until2p23(s26))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11692, 11691])).
% 1.78/1.71 tff(11694,plain,
% 1.78/1.71 (xuntil2p24(s26) | (~until2p23(s26))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11693, 10867, 9781])).
% 1.78/1.71 tff(11695,plain,
% 1.78/1.71 (~until2p23(s26)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11694, 11690])).
% 1.78/1.71 tff(11696,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s25, s26)) | until2p23(s26) | (~xuntil2p24(s25)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s25, s26)) | until2p23(s26) | (~xuntil2p24(s25)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11697,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s25, s26)) | until2p23(s26) | (~xuntil2p24(s25)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11698,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s25, s26)) | until2p23(s26) | (~xuntil2p24(s25))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11697, 11696])).
% 1.78/1.71 tff(11699,plain,
% 1.78/1.71 (until2p23(s26) | (~xuntil2p24(s25))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11698, 2455, 10882])).
% 1.78/1.71 tff(11700,plain,
% 1.78/1.71 (~xuntil2p24(s25)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11699, 11695])).
% 1.78/1.71 tff(11701,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s25) | xuntil2p24(s25) | (~until2p23(s25)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s25) | xuntil2p24(s25) | (~until2p23(s25)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11702,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s25) | xuntil2p24(s25) | (~until2p23(s25)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11703,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s25) | xuntil2p24(s25) | (~until2p23(s25))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11702, 11701])).
% 1.78/1.71 tff(11704,plain,
% 1.78/1.71 (xuntil2p24(s25) | (~until2p23(s25))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11703, 10867, 9203])).
% 1.78/1.71 tff(11705,plain,
% 1.78/1.71 (~until2p23(s25)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11704, 11700])).
% 1.78/1.71 tff(11706,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s24, s25)) | until2p23(s25) | (~xuntil2p24(s24)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s24, s25)) | until2p23(s25) | (~xuntil2p24(s24)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11707,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s24, s25)) | until2p23(s25) | (~xuntil2p24(s24)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11708,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s24, s25)) | until2p23(s25) | (~xuntil2p24(s24))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11707, 11706])).
% 1.78/1.71 tff(11709,plain,
% 1.78/1.71 (until2p23(s25) | (~xuntil2p24(s24))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11708, 2388, 10882])).
% 1.78/1.71 tff(11710,plain,
% 1.78/1.71 (~xuntil2p24(s24)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11709, 11705])).
% 1.78/1.71 tff(11711,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s24) | xuntil2p24(s24) | (~until2p23(s24)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s24) | xuntil2p24(s24) | (~until2p23(s24)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11712,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s24) | xuntil2p24(s24) | (~until2p23(s24)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11713,plain,
% 1.78/1.71 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s24) | xuntil2p24(s24) | (~until2p23(s24))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11712, 11711])).
% 1.78/1.71 tff(11714,plain,
% 1.78/1.71 (xuntil2p24(s24) | (~until2p23(s24))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11713, 10867, 9212])).
% 1.78/1.71 tff(11715,plain,
% 1.78/1.71 (~until2p23(s24)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11714, 11710])).
% 1.78/1.71 tff(11716,assumption,(~until2p23(s24)), introduced(assumption)).
% 1.78/1.71 tff(11717,assumption,(trans(s104, s24)), introduced(assumption)).
% 1.78/1.71 tff(11718,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11719,plain,
% 1.78/1.71 (((~trans(s104, s24)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s24)) <=> (until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11720,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s24)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24))))),
% 1.78/1.71 inference(monotonicity,[status(thm)],[11719])).
% 1.78/1.71 tff(11721,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s24)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24)))),
% 1.78/1.71 inference(transitivity,[status(thm)],[11720, 11718])).
% 1.78/1.71 tff(11722,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s24)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s24))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11723,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s24) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s24))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11722, 11721])).
% 1.78/1.71 tff(11724,plain,
% 1.78/1.71 ($false),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11723, 10853, 11717, 11532, 11716, 11533])).
% 1.78/1.71 tff(11725,plain,((~trans(s104, s24)) | until2p23(s24) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.71 tff(11726,plain,
% 1.78/1.71 (~trans(s104, s24)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11725, 11715, 10843])).
% 1.78/1.71 tff(11727,plain,
% 1.78/1.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s23, s24)) | until2p23(s24) | (~xuntil2p24(s23)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s23, s24)) | until2p23(s24) | (~xuntil2p24(s23)))),
% 1.78/1.71 inference(rewrite,[status(thm)],[])).
% 1.78/1.71 tff(11728,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s23, s24)) | until2p23(s24) | (~xuntil2p24(s23)))),
% 1.78/1.71 inference(quant_inst,[status(thm)],[])).
% 1.78/1.71 tff(11729,plain,
% 1.78/1.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s23, s24)) | until2p23(s24) | (~xuntil2p24(s23))),
% 1.78/1.71 inference(modus_ponens,[status(thm)],[11728, 11727])).
% 1.78/1.71 tff(11730,plain,
% 1.78/1.71 (until2p23(s24) | (~xuntil2p24(s23))),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11729, 2299, 10882])).
% 1.78/1.71 tff(11731,plain,
% 1.78/1.71 (~xuntil2p24(s23)),
% 1.78/1.71 inference(unit_resolution,[status(thm)],[11730, 11715])).
% 1.78/1.71 tff(11732,plain,
% 1.78/1.71 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s23) | xuntil2p24(s23) | (~until2p23(s23)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s23) | xuntil2p24(s23) | (~until2p23(s23)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11733,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s23) | xuntil2p24(s23) | (~until2p23(s23)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11734,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s23) | xuntil2p24(s23) | (~until2p23(s23))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11733, 11732])).
% 1.78/1.72 tff(11735,plain,
% 1.78/1.72 (xuntil2p24(s23) | (~until2p23(s23))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11734, 10867, 9220])).
% 1.78/1.72 tff(11736,plain,
% 1.78/1.72 (~until2p23(s23)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11735, 11731])).
% 1.78/1.72 tff(11737,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s22, s23)) | until2p23(s23) | (~xuntil2p24(s22)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s22, s23)) | until2p23(s23) | (~xuntil2p24(s22)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11738,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s22, s23)) | until2p23(s23) | (~xuntil2p24(s22)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11739,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s22, s23)) | until2p23(s23) | (~xuntil2p24(s22))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11738, 11737])).
% 1.78/1.72 tff(11740,plain,
% 1.78/1.72 (until2p23(s23) | (~xuntil2p24(s22))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11739, 2224, 10882])).
% 1.78/1.72 tff(11741,plain,
% 1.78/1.72 (~xuntil2p24(s22)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11740, 11736])).
% 1.78/1.72 tff(11742,plain,
% 1.78/1.72 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s22) | xuntil2p24(s22) | (~until2p23(s22)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s22) | xuntil2p24(s22) | (~until2p23(s22)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11743,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s22) | xuntil2p24(s22) | (~until2p23(s22)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11744,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s22) | xuntil2p24(s22) | (~until2p23(s22))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11743, 11742])).
% 1.78/1.72 tff(11745,plain,
% 1.78/1.72 (xuntil2p24(s22) | (~until2p23(s22))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11744, 10867, 9727])).
% 1.78/1.72 tff(11746,plain,
% 1.78/1.72 (~until2p23(s22)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11745, 11741])).
% 1.78/1.72 tff(11747,assumption,(~until2p23(s22)), introduced(assumption)).
% 1.78/1.72 tff(11748,assumption,(trans(s104, s22)), introduced(assumption)).
% 1.78/1.72 tff(11749,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11750,plain,
% 1.78/1.72 (((~trans(s104, s22)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s22)) <=> (until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11751,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s22)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11750])).
% 1.78/1.72 tff(11752,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s22)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11751, 11749])).
% 1.78/1.72 tff(11753,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s22)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s22))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11754,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s22) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s22))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11753, 11752])).
% 1.78/1.72 tff(11755,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11754, 10853, 11748, 11532, 11747, 11533])).
% 1.78/1.72 tff(11756,plain,((~trans(s104, s22)) | until2p23(s22) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11757,plain,
% 1.78/1.72 (~trans(s104, s22)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11756, 11746, 10843])).
% 1.78/1.72 tff(11758,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s21, s22)) | until2p23(s22) | (~xuntil2p24(s21)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s21, s22)) | until2p23(s22) | (~xuntil2p24(s21)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11759,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s21, s22)) | until2p23(s22) | (~xuntil2p24(s21)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11760,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s21, s22)) | until2p23(s22) | (~xuntil2p24(s21))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11759, 11758])).
% 1.78/1.72 tff(11761,plain,
% 1.78/1.72 (until2p23(s22) | (~xuntil2p24(s21))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11760, 2160, 10882])).
% 1.78/1.72 tff(11762,plain,
% 1.78/1.72 (~xuntil2p24(s21)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11761, 11746])).
% 1.78/1.72 tff(11763,plain,
% 1.78/1.72 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s21) | xuntil2p24(s21) | (~until2p23(s21)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s21) | xuntil2p24(s21) | (~until2p23(s21)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11764,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s21) | xuntil2p24(s21) | (~until2p23(s21)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11765,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s21) | xuntil2p24(s21) | (~until2p23(s21))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11764, 11763])).
% 1.78/1.72 tff(11766,plain,
% 1.78/1.72 (xuntil2p24(s21) | (~until2p23(s21))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11765, 10867, 9236])).
% 1.78/1.72 tff(11767,plain,
% 1.78/1.72 (~until2p23(s21)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11766, 11762])).
% 1.78/1.72 tff(11768,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s20, s21)) | until2p23(s21) | (~xuntil2p24(s20)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s20, s21)) | until2p23(s21) | (~xuntil2p24(s20)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11769,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s20, s21)) | until2p23(s21) | (~xuntil2p24(s20)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11770,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s20, s21)) | until2p23(s21) | (~xuntil2p24(s20))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11769, 11768])).
% 1.78/1.72 tff(11771,plain,
% 1.78/1.72 (until2p23(s21) | (~xuntil2p24(s20))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11770, 2065, 10882])).
% 1.78/1.72 tff(11772,plain,
% 1.78/1.72 (~xuntil2p24(s20)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11771, 11767])).
% 1.78/1.72 tff(11773,plain,
% 1.78/1.72 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s20) | xuntil2p24(s20) | (~until2p23(s20)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s20) | xuntil2p24(s20) | (~until2p23(s20)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11774,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s20) | xuntil2p24(s20) | (~until2p23(s20)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11775,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s20) | xuntil2p24(s20) | (~until2p23(s20))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11774, 11773])).
% 1.78/1.72 tff(11776,plain,
% 1.78/1.72 (xuntil2p24(s20) | (~until2p23(s20))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11775, 10867, 9245])).
% 1.78/1.72 tff(11777,plain,
% 1.78/1.72 (~until2p23(s20)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11776, 11772])).
% 1.78/1.72 tff(11778,assumption,(~until2p23(s20)), introduced(assumption)).
% 1.78/1.72 tff(11779,assumption,(trans(s104, s20)), introduced(assumption)).
% 1.78/1.72 tff(11780,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11781,plain,
% 1.78/1.72 (((~trans(s104, s20)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s20)) <=> (until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11782,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s20)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11781])).
% 1.78/1.72 tff(11783,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s20)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11782, 11780])).
% 1.78/1.72 tff(11784,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s20)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s20))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11785,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s20) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s20))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11784, 11783])).
% 1.78/1.72 tff(11786,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11785, 10853, 11779, 11532, 11778, 11533])).
% 1.78/1.72 tff(11787,plain,((~trans(s104, s20)) | until2p23(s20) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11788,plain,
% 1.78/1.72 (~trans(s104, s20)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11787, 11777, 10843])).
% 1.78/1.72 tff(11789,assumption,(~until2p23(s103)), introduced(assumption)).
% 1.78/1.72 tff(11790,assumption,(trans(s104, s103)), introduced(assumption)).
% 1.78/1.72 tff(11791,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11792,plain,
% 1.78/1.72 (((~trans(s104, s103)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s103)) <=> (until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11793,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s103)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s103))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11792])).
% 1.78/1.72 tff(11794,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s103)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s103))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11793, 11791])).
% 1.78/1.72 tff(11795,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s103)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s103))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11796,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s103) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s103))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11795, 11794])).
% 1.78/1.72 tff(11797,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11796, 10853, 11790, 11532, 11789, 11533])).
% 1.78/1.72 tff(11798,plain,((~trans(s104, s103)) | until2p23(s103) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11799,plain,
% 1.78/1.72 (~trans(s104, s103)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11798, 10892, 10843])).
% 1.78/1.72 tff(11800,assumption,(~until2p23(s78)), introduced(assumption)).
% 1.78/1.72 tff(11801,assumption,(trans(s104, s78)), introduced(assumption)).
% 1.78/1.72 tff(11802,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11803,plain,
% 1.78/1.72 (((~trans(s104, s78)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s78)) <=> (until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11804,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s78)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11803])).
% 1.78/1.72 tff(11805,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s78)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11804, 11802])).
% 1.78/1.72 tff(11806,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s78)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s78))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11807,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s78) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s78))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11806, 11805])).
% 1.78/1.72 tff(11808,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11807, 10853, 11801, 11532, 11800, 11533])).
% 1.78/1.72 tff(11809,plain,((~trans(s104, s78)) | until2p23(s78) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11810,plain,
% 1.78/1.72 (~trans(s104, s78)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11809, 11142, 10843])).
% 1.78/1.72 tff(11811,assumption,(~until2p23(s38)), introduced(assumption)).
% 1.78/1.72 tff(11812,assumption,(trans(s104, s38)), introduced(assumption)).
% 1.78/1.72 tff(11813,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11814,plain,
% 1.78/1.72 (((~trans(s104, s38)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s38)) <=> (until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11815,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s38)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11814])).
% 1.78/1.72 tff(11816,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s38)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11815, 11813])).
% 1.78/1.72 tff(11817,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s38)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s38))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11818,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s38) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s38))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11817, 11816])).
% 1.78/1.72 tff(11819,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11818, 10853, 11812, 11532, 11811, 11533])).
% 1.78/1.72 tff(11820,plain,((~trans(s104, s38)) | until2p23(s38) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11821,plain,
% 1.78/1.72 (~trans(s104, s38)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11820, 11564, 10843])).
% 1.78/1.72 tff(11822,assumption,(~until2p23(s97)), introduced(assumption)).
% 1.78/1.72 tff(11823,assumption,(trans(s104, s97)), introduced(assumption)).
% 1.78/1.72 tff(11824,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11825,plain,
% 1.78/1.72 (((~trans(s104, s97)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s97)) <=> (until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11826,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s97)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11825])).
% 1.78/1.72 tff(11827,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s97)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11826, 11824])).
% 1.78/1.72 tff(11828,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s97)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s97))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11829,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s97) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s97))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11828, 11827])).
% 1.78/1.72 tff(11830,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11829, 10853, 11823, 11532, 11822, 11533])).
% 1.78/1.72 tff(11831,plain,((~trans(s104, s97)) | until2p23(s97) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11832,plain,
% 1.78/1.72 (~trans(s104, s97)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11831, 10952, 10843])).
% 1.78/1.72 tff(11833,assumption,(~until2p23(s72)), introduced(assumption)).
% 1.78/1.72 tff(11834,assumption,(trans(s104, s72)), introduced(assumption)).
% 1.78/1.72 tff(11835,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11836,plain,
% 1.78/1.72 (((~trans(s104, s72)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s72)) <=> (until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11837,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s72)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11836])).
% 1.78/1.72 tff(11838,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s72)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11837, 11835])).
% 1.78/1.72 tff(11839,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s72)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s72))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11840,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s72) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s72))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11839, 11838])).
% 1.78/1.72 tff(11841,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11840, 10853, 11834, 11532, 11833, 11533])).
% 1.78/1.72 tff(11842,plain,((~trans(s104, s72)) | until2p23(s72) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11843,plain,
% 1.78/1.72 (~trans(s104, s72)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11842, 11202, 10843])).
% 1.78/1.72 tff(11844,assumption,(~until2p23(s35)), introduced(assumption)).
% 1.78/1.72 tff(11845,assumption,(trans(s104, s35)), introduced(assumption)).
% 1.78/1.72 tff(11846,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11847,plain,
% 1.78/1.72 (((~trans(s104, s35)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s35)) <=> (until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11848,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s35)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11847])).
% 1.78/1.72 tff(11849,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s35)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11848, 11846])).
% 1.78/1.72 tff(11850,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s35)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s35))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11851,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s35) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s35))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11850, 11849])).
% 1.78/1.72 tff(11852,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11851, 10853, 11845, 11532, 11844, 11533])).
% 1.78/1.72 tff(11853,plain,((~trans(s104, s35)) | until2p23(s35) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11854,plain,
% 1.78/1.72 (~trans(s104, s35)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11853, 11594, 10843])).
% 1.78/1.72 tff(11855,assumption,(~until2p23(s66)), introduced(assumption)).
% 1.78/1.72 tff(11856,assumption,(trans(s104, s66)), introduced(assumption)).
% 1.78/1.72 tff(11857,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11858,plain,
% 1.78/1.72 (((~trans(s104, s66)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s66)) <=> (until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11859,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s66)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11858])).
% 1.78/1.72 tff(11860,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s66)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11859, 11857])).
% 1.78/1.72 tff(11861,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s66)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s66))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11862,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s66) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s66))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11861, 11860])).
% 1.78/1.72 tff(11863,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11862, 10853, 11856, 11532, 11855, 11533])).
% 1.78/1.72 tff(11864,plain,((~trans(s104, s66)) | until2p23(s66) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11865,plain,
% 1.78/1.72 (~trans(s104, s66)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11864, 11262, 10843])).
% 1.78/1.72 tff(11866,assumption,(~until2p23(s68)), introduced(assumption)).
% 1.78/1.72 tff(11867,assumption,(trans(s104, s68)), introduced(assumption)).
% 1.78/1.72 tff(11868,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11869,plain,
% 1.78/1.72 (((~trans(s104, s68)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s68)) <=> (until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11870,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s68)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68))))),
% 1.78/1.72 inference(monotonicity,[status(thm)],[11869])).
% 1.78/1.72 tff(11871,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s68)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68)))),
% 1.78/1.72 inference(transitivity,[status(thm)],[11870, 11868])).
% 1.78/1.72 tff(11872,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s68)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s68))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11873,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s68) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s68))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11872, 11871])).
% 1.78/1.72 tff(11874,plain,
% 1.78/1.72 ($false),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11873, 10853, 11867, 11532, 11866, 11533])).
% 1.78/1.72 tff(11875,plain,((~trans(s104, s68)) | until2p23(s68) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.72 tff(11876,plain,
% 1.78/1.72 (~trans(s104, s68)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11875, 11242, 10843])).
% 1.78/1.72 tff(11877,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s19, s20)) | until2p23(s20) | (~xuntil2p24(s19)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s19, s20)) | until2p23(s20) | (~xuntil2p24(s19)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11878,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s19, s20)) | until2p23(s20) | (~xuntil2p24(s19)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11879,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s19, s20)) | until2p23(s20) | (~xuntil2p24(s19))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11878, 11877])).
% 1.78/1.72 tff(11880,plain,
% 1.78/1.72 (until2p23(s20) | (~xuntil2p24(s19))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11879, 2004, 10882])).
% 1.78/1.72 tff(11881,plain,
% 1.78/1.72 (~xuntil2p24(s19)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11880, 11777])).
% 1.78/1.72 tff(11882,plain,
% 1.78/1.72 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s19) | xuntil2p24(s19) | (~until2p23(s19)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s19) | xuntil2p24(s19) | (~until2p23(s19)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11883,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s19) | xuntil2p24(s19) | (~until2p23(s19)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11884,plain,
% 1.78/1.72 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s19) | xuntil2p24(s19) | (~until2p23(s19))),
% 1.78/1.72 inference(modus_ponens,[status(thm)],[11883, 11882])).
% 1.78/1.72 tff(11885,plain,
% 1.78/1.72 (xuntil2p24(s19) | (~until2p23(s19))),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11884, 10867, 9253])).
% 1.78/1.72 tff(11886,plain,
% 1.78/1.72 (~until2p23(s19)),
% 1.78/1.72 inference(unit_resolution,[status(thm)],[11885, 11881])).
% 1.78/1.72 tff(11887,plain,
% 1.78/1.72 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s18, s19)) | until2p23(s19) | (~xuntil2p24(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s18, s19)) | until2p23(s19) | (~xuntil2p24(s18)))),
% 1.78/1.72 inference(rewrite,[status(thm)],[])).
% 1.78/1.72 tff(11888,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s18, s19)) | until2p23(s19) | (~xuntil2p24(s18)))),
% 1.78/1.72 inference(quant_inst,[status(thm)],[])).
% 1.78/1.72 tff(11889,plain,
% 1.78/1.72 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s18, s19)) | until2p23(s19) | (~xuntil2p24(s18))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11888, 11887])).
% 1.78/1.73 tff(11890,plain,
% 1.78/1.73 (until2p23(s19) | (~xuntil2p24(s18))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11889, 1926, 10882])).
% 1.78/1.73 tff(11891,plain,
% 1.78/1.73 (~xuntil2p24(s18)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11890, 11886])).
% 1.78/1.73 tff(11892,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s18) | xuntil2p24(s18) | (~until2p23(s18)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s18) | xuntil2p24(s18) | (~until2p23(s18)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11893,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s18) | xuntil2p24(s18) | (~until2p23(s18)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11894,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s18) | xuntil2p24(s18) | (~until2p23(s18))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11893, 11892])).
% 1.78/1.73 tff(11895,plain,
% 1.78/1.73 (xuntil2p24(s18) | (~until2p23(s18))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11894, 10867, 9673])).
% 1.78/1.73 tff(11896,plain,
% 1.78/1.73 (~until2p23(s18)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11895, 11891])).
% 1.78/1.73 tff(11897,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s17, s18)) | until2p23(s18) | (~xuntil2p24(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s17, s18)) | until2p23(s18) | (~xuntil2p24(s17)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11898,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s17, s18)) | until2p23(s18) | (~xuntil2p24(s17)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11899,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s17, s18)) | until2p23(s18) | (~xuntil2p24(s17))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11898, 11897])).
% 1.78/1.73 tff(11900,plain,
% 1.78/1.73 (until2p23(s18) | (~xuntil2p24(s17))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11899, 1827, 10882])).
% 1.78/1.73 tff(11901,plain,
% 1.78/1.73 (~xuntil2p24(s17)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11900, 11896])).
% 1.78/1.73 tff(11902,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s17) | xuntil2p24(s17) | (~until2p23(s17)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s17) | xuntil2p24(s17) | (~until2p23(s17)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11903,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s17) | xuntil2p24(s17) | (~until2p23(s17)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11904,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s17) | xuntil2p24(s17) | (~until2p23(s17))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11903, 11902])).
% 1.78/1.73 tff(11905,plain,
% 1.78/1.73 (xuntil2p24(s17) | (~until2p23(s17))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11904, 10867, 9269])).
% 1.78/1.73 tff(11906,plain,
% 1.78/1.73 (~until2p23(s17)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11905, 11901])).
% 1.78/1.73 tff(11907,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s16, s17)) | until2p23(s17) | (~xuntil2p24(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s16, s17)) | until2p23(s17) | (~xuntil2p24(s16)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11908,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s16, s17)) | until2p23(s17) | (~xuntil2p24(s16)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11909,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s16, s17)) | until2p23(s17) | (~xuntil2p24(s16))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11908, 11907])).
% 1.78/1.73 tff(11910,plain,
% 1.78/1.73 (until2p23(s17) | (~xuntil2p24(s16))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11909, 1760, 10882])).
% 1.78/1.73 tff(11911,plain,
% 1.78/1.73 (~xuntil2p24(s16)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11910, 11906])).
% 1.78/1.73 tff(11912,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s16) | xuntil2p24(s16) | (~until2p23(s16)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s16) | xuntil2p24(s16) | (~until2p23(s16)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11913,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s16) | xuntil2p24(s16) | (~until2p23(s16)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11914,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s16) | xuntil2p24(s16) | (~until2p23(s16))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11913, 11912])).
% 1.78/1.73 tff(11915,plain,
% 1.78/1.73 (xuntil2p24(s16) | (~until2p23(s16))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11914, 10867, 9278])).
% 1.78/1.73 tff(11916,plain,
% 1.78/1.73 (~until2p23(s16)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11915, 11911])).
% 1.78/1.73 tff(11917,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s15, s16)) | until2p23(s16) | (~xuntil2p24(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s15, s16)) | until2p23(s16) | (~xuntil2p24(s15)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11918,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s15, s16)) | until2p23(s16) | (~xuntil2p24(s15)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11919,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s15, s16)) | until2p23(s16) | (~xuntil2p24(s15))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11918, 11917])).
% 1.78/1.73 tff(11920,plain,
% 1.78/1.73 (until2p23(s16) | (~xuntil2p24(s15))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11919, 1671, 10882])).
% 1.78/1.73 tff(11921,plain,
% 1.78/1.73 (~xuntil2p24(s15)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11920, 11916])).
% 1.78/1.73 tff(11922,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s15) | xuntil2p24(s15) | (~until2p23(s15)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s15) | xuntil2p24(s15) | (~until2p23(s15)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11923,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s15) | xuntil2p24(s15) | (~until2p23(s15)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11924,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s15) | xuntil2p24(s15) | (~until2p23(s15))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11923, 11922])).
% 1.78/1.73 tff(11925,plain,
% 1.78/1.73 (xuntil2p24(s15) | (~until2p23(s15))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11924, 10867, 9286])).
% 1.78/1.73 tff(11926,plain,
% 1.78/1.73 (~until2p23(s15)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11925, 11921])).
% 1.78/1.73 tff(11927,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s14, s15)) | until2p23(s15) | (~xuntil2p24(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s14, s15)) | until2p23(s15) | (~xuntil2p24(s14)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11928,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s14, s15)) | until2p23(s15) | (~xuntil2p24(s14)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11929,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s14, s15)) | until2p23(s15) | (~xuntil2p24(s14))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11928, 11927])).
% 1.78/1.73 tff(11930,plain,
% 1.78/1.73 (until2p23(s15) | (~xuntil2p24(s14))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11929, 1596, 10882])).
% 1.78/1.73 tff(11931,plain,
% 1.78/1.73 (~xuntil2p24(s14)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11930, 11926])).
% 1.78/1.73 tff(11932,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s14) | xuntil2p24(s14) | (~until2p23(s14)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s14) | xuntil2p24(s14) | (~until2p23(s14)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11933,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s14) | xuntil2p24(s14) | (~until2p23(s14)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11934,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s14) | xuntil2p24(s14) | (~until2p23(s14))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11933, 11932])).
% 1.78/1.73 tff(11935,plain,
% 1.78/1.73 (xuntil2p24(s14) | (~until2p23(s14))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11934, 10867, 9619])).
% 1.78/1.73 tff(11936,plain,
% 1.78/1.73 (~until2p23(s14)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11935, 11931])).
% 1.78/1.73 tff(11937,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s13, s14)) | until2p23(s14) | (~xuntil2p24(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s13, s14)) | until2p23(s14) | (~xuntil2p24(s13)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11938,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s13, s14)) | until2p23(s14) | (~xuntil2p24(s13)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11939,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s13, s14)) | until2p23(s14) | (~xuntil2p24(s13))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11938, 11937])).
% 1.78/1.73 tff(11940,plain,
% 1.78/1.73 (until2p23(s14) | (~xuntil2p24(s13))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11939, 1532, 10882])).
% 1.78/1.73 tff(11941,plain,
% 1.78/1.73 (~xuntil2p24(s13)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11940, 11936])).
% 1.78/1.73 tff(11942,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s13) | xuntil2p24(s13) | (~until2p23(s13)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s13) | xuntil2p24(s13) | (~until2p23(s13)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11943,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s13) | xuntil2p24(s13) | (~until2p23(s13)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11944,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s13) | xuntil2p24(s13) | (~until2p23(s13))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11943, 11942])).
% 1.78/1.73 tff(11945,plain,
% 1.78/1.73 (xuntil2p24(s13) | (~until2p23(s13))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11944, 10867, 9302])).
% 1.78/1.73 tff(11946,plain,
% 1.78/1.73 (~until2p23(s13)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11945, 11941])).
% 1.78/1.73 tff(11947,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s12, s13)) | until2p23(s13) | (~xuntil2p24(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s12, s13)) | until2p23(s13) | (~xuntil2p24(s12)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11948,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s12, s13)) | until2p23(s13) | (~xuntil2p24(s12)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11949,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s12, s13)) | until2p23(s13) | (~xuntil2p24(s12))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11948, 11947])).
% 1.78/1.73 tff(11950,plain,
% 1.78/1.73 (until2p23(s13) | (~xuntil2p24(s12))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11949, 1437, 10882])).
% 1.78/1.73 tff(11951,plain,
% 1.78/1.73 (~xuntil2p24(s12)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11950, 11946])).
% 1.78/1.73 tff(11952,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s12) | xuntil2p24(s12) | (~until2p23(s12)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s12) | xuntil2p24(s12) | (~until2p23(s12)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11953,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s12) | xuntil2p24(s12) | (~until2p23(s12)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11954,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s12) | xuntil2p24(s12) | (~until2p23(s12))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11953, 11952])).
% 1.78/1.73 tff(11955,plain,
% 1.78/1.73 (xuntil2p24(s12) | (~until2p23(s12))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11954, 10867, 9311])).
% 1.78/1.73 tff(11956,plain,
% 1.78/1.73 (~until2p23(s12)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11955, 11951])).
% 1.78/1.73 tff(11957,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s11, s12)) | until2p23(s12) | (~xuntil2p24(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s11, s12)) | until2p23(s12) | (~xuntil2p24(s11)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11958,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s11, s12)) | until2p23(s12) | (~xuntil2p24(s11)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11959,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s11, s12)) | until2p23(s12) | (~xuntil2p24(s11))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11958, 11957])).
% 1.78/1.73 tff(11960,plain,
% 1.78/1.73 (until2p23(s12) | (~xuntil2p24(s11))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11959, 1376, 10882])).
% 1.78/1.73 tff(11961,plain,
% 1.78/1.73 (~xuntil2p24(s11)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11960, 11956])).
% 1.78/1.73 tff(11962,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s11) | xuntil2p24(s11) | (~until2p23(s11)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s11) | xuntil2p24(s11) | (~until2p23(s11)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11963,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s11) | xuntil2p24(s11) | (~until2p23(s11)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11964,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s11) | xuntil2p24(s11) | (~until2p23(s11))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11963, 11962])).
% 1.78/1.73 tff(11965,plain,
% 1.78/1.73 (xuntil2p24(s11) | (~until2p23(s11))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11964, 10867, 9319])).
% 1.78/1.73 tff(11966,plain,
% 1.78/1.73 (~until2p23(s11)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11965, 11961])).
% 1.78/1.73 tff(11967,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s10, s11)) | until2p23(s11) | (~xuntil2p24(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s10, s11)) | until2p23(s11) | (~xuntil2p24(s10)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11968,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s10, s11)) | until2p23(s11) | (~xuntil2p24(s10)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11969,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s10, s11)) | until2p23(s11) | (~xuntil2p24(s10))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11968, 11967])).
% 1.78/1.73 tff(11970,plain,
% 1.78/1.73 (until2p23(s11) | (~xuntil2p24(s10))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11969, 1298, 10882])).
% 1.78/1.73 tff(11971,plain,
% 1.78/1.73 (~xuntil2p24(s10)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11970, 11966])).
% 1.78/1.73 tff(11972,plain,
% 1.78/1.73 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s10) | xuntil2p24(s10) | (~until2p23(s10)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s10) | xuntil2p24(s10) | (~until2p23(s10)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11973,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s10) | xuntil2p24(s10) | (~until2p23(s10)))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11974,plain,
% 1.78/1.73 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s10) | xuntil2p24(s10) | (~until2p23(s10))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11973, 11972])).
% 1.78/1.73 tff(11975,plain,
% 1.78/1.73 (xuntil2p24(s10) | (~until2p23(s10))),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11974, 10867, 9565])).
% 1.78/1.73 tff(11976,plain,
% 1.78/1.73 (~until2p23(s10)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11975, 11971])).
% 1.78/1.73 tff(11977,assumption,(~until2p23(s10)), introduced(assumption)).
% 1.78/1.73 tff(11978,assumption,(trans(s104, s10)), introduced(assumption)).
% 1.78/1.73 tff(11979,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11980,plain,
% 1.78/1.73 (((~trans(s104, s10)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s10)) <=> (until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11981,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s10)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[11980])).
% 1.78/1.73 tff(11982,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s10)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[11981, 11979])).
% 1.78/1.73 tff(11983,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s10)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s10))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11984,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s10) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s10))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11983, 11982])).
% 1.78/1.73 tff(11985,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11984, 10853, 11978, 11532, 11977, 11533])).
% 1.78/1.73 tff(11986,plain,((~trans(s104, s10)) | until2p23(s10) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(11987,plain,
% 1.78/1.73 (~trans(s104, s10)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11986, 11976, 10843])).
% 1.78/1.73 tff(11988,assumption,(~until2p23(s23)), introduced(assumption)).
% 1.78/1.73 tff(11989,assumption,(trans(s104, s23)), introduced(assumption)).
% 1.78/1.73 tff(11990,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11991,plain,
% 1.78/1.73 (((~trans(s104, s23)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s23)) <=> (until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(11992,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s23)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[11991])).
% 1.78/1.73 tff(11993,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s23)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[11992, 11990])).
% 1.78/1.73 tff(11994,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s23)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s23))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(11995,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s23) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s23))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[11994, 11993])).
% 1.78/1.73 tff(11996,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11995, 10853, 11989, 11532, 11988, 11533])).
% 1.78/1.73 tff(11997,plain,((~trans(s104, s23)) | until2p23(s23) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(11998,plain,
% 1.78/1.73 (~trans(s104, s23)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[11997, 11736, 10843])).
% 1.78/1.73 tff(11999,assumption,(~until2p23(s74)), introduced(assumption)).
% 1.78/1.73 tff(12000,assumption,(trans(s104, s74)), introduced(assumption)).
% 1.78/1.73 tff(12001,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12002,plain,
% 1.78/1.73 (((~trans(s104, s74)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s74)) <=> (until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12003,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s74)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[12002])).
% 1.78/1.73 tff(12004,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s74)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[12003, 12001])).
% 1.78/1.73 tff(12005,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s74)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s74))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(12006,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s74) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s74))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[12005, 12004])).
% 1.78/1.73 tff(12007,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12006, 10853, 12000, 11532, 11999, 11533])).
% 1.78/1.73 tff(12008,plain,((~trans(s104, s74)) | until2p23(s74) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(12009,plain,
% 1.78/1.73 (~trans(s104, s74)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12008, 11182, 10843])).
% 1.78/1.73 tff(12010,assumption,(~until2p23(s96)), introduced(assumption)).
% 1.78/1.73 tff(12011,assumption,(trans(s104, s96)), introduced(assumption)).
% 1.78/1.73 tff(12012,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12013,plain,
% 1.78/1.73 (((~trans(s104, s96)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s96)) <=> (until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12014,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s96)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[12013])).
% 1.78/1.73 tff(12015,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s96)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[12014, 12012])).
% 1.78/1.73 tff(12016,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s96)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s96))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(12017,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s96) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s96))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[12016, 12015])).
% 1.78/1.73 tff(12018,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12017, 10853, 12011, 11532, 12010, 11533])).
% 1.78/1.73 tff(12019,plain,((~trans(s104, s96)) | until2p23(s96) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(12020,plain,
% 1.78/1.73 (~trans(s104, s96)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12019, 10962, 10843])).
% 1.78/1.73 tff(12021,assumption,(~until2p23(s16)), introduced(assumption)).
% 1.78/1.73 tff(12022,assumption,(trans(s104, s16)), introduced(assumption)).
% 1.78/1.73 tff(12023,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12024,plain,
% 1.78/1.73 (((~trans(s104, s16)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s16)) <=> (until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12025,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s16)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[12024])).
% 1.78/1.73 tff(12026,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s16)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[12025, 12023])).
% 1.78/1.73 tff(12027,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s16)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s16))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(12028,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s16) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s16))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[12027, 12026])).
% 1.78/1.73 tff(12029,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12028, 10853, 12022, 11532, 12021, 11533])).
% 1.78/1.73 tff(12030,plain,((~trans(s104, s16)) | until2p23(s16) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(12031,plain,
% 1.78/1.73 (~trans(s104, s16)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12030, 11916, 10843])).
% 1.78/1.73 tff(12032,assumption,(~until2p23(s81)), introduced(assumption)).
% 1.78/1.73 tff(12033,assumption,(trans(s104, s81)), introduced(assumption)).
% 1.78/1.73 tff(12034,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12035,plain,
% 1.78/1.73 (((~trans(s104, s81)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s81)) <=> (until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12036,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s81)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[12035])).
% 1.78/1.73 tff(12037,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s81)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[12036, 12034])).
% 1.78/1.73 tff(12038,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s81)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s81))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(12039,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s81) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s81))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[12038, 12037])).
% 1.78/1.73 tff(12040,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12039, 10853, 12033, 11532, 12032, 11533])).
% 1.78/1.73 tff(12041,plain,((~trans(s104, s81)) | until2p23(s81) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.73 tff(12042,plain,
% 1.78/1.73 (~trans(s104, s81)),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12041, 11112, 10843])).
% 1.78/1.73 tff(12043,assumption,(~until2p23(s19)), introduced(assumption)).
% 1.78/1.73 tff(12044,assumption,(trans(s104, s19)), introduced(assumption)).
% 1.78/1.73 tff(12045,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12046,plain,
% 1.78/1.73 (((~trans(s104, s19)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s19)) <=> (until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19)))),
% 1.78/1.73 inference(rewrite,[status(thm)],[])).
% 1.78/1.73 tff(12047,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s19)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19))))),
% 1.78/1.73 inference(monotonicity,[status(thm)],[12046])).
% 1.78/1.73 tff(12048,plain,
% 1.78/1.73 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s19)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19)))),
% 1.78/1.73 inference(transitivity,[status(thm)],[12047, 12045])).
% 1.78/1.73 tff(12049,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s19)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s19))),
% 1.78/1.73 inference(quant_inst,[status(thm)],[])).
% 1.78/1.73 tff(12050,plain,
% 1.78/1.73 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s19) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s19))),
% 1.78/1.73 inference(modus_ponens,[status(thm)],[12049, 12048])).
% 1.78/1.73 tff(12051,plain,
% 1.78/1.73 ($false),
% 1.78/1.73 inference(unit_resolution,[status(thm)],[12050, 10853, 12044, 11532, 12043, 11533])).
% 1.78/1.73 tff(12052,plain,((~trans(s104, s19)) | until2p23(s19) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12053,plain,
% 1.78/1.74 (~trans(s104, s19)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12052, 11886, 10843])).
% 1.78/1.74 tff(12054,assumption,(~until2p23(s54)), introduced(assumption)).
% 1.78/1.74 tff(12055,assumption,(trans(s104, s54)), introduced(assumption)).
% 1.78/1.74 tff(12056,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12057,plain,
% 1.78/1.74 (((~trans(s104, s54)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s54)) <=> (until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12058,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s54)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12057])).
% 1.78/1.74 tff(12059,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s54)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12058, 12056])).
% 1.78/1.74 tff(12060,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s54)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s54))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12061,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s54) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s54))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12060, 12059])).
% 1.78/1.74 tff(12062,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12061, 10853, 12055, 11532, 12054, 11533])).
% 1.78/1.74 tff(12063,plain,((~trans(s104, s54)) | until2p23(s54) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12064,plain,
% 1.78/1.74 (~trans(s104, s54)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12063, 11382, 10843])).
% 1.78/1.74 tff(12065,assumption,(~until2p23(s88)), introduced(assumption)).
% 1.78/1.74 tff(12066,assumption,(trans(s104, s88)), introduced(assumption)).
% 1.78/1.74 tff(12067,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12068,plain,
% 1.78/1.74 (((~trans(s104, s88)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s88)) <=> (until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12069,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s88)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12068])).
% 1.78/1.74 tff(12070,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s88)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12069, 12067])).
% 1.78/1.74 tff(12071,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s88)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s88))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12072,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s88) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s88))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12071, 12070])).
% 1.78/1.74 tff(12073,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12072, 10853, 12066, 11532, 12065, 11533])).
% 1.78/1.74 tff(12074,plain,((~trans(s104, s88)) | until2p23(s88) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12075,plain,
% 1.78/1.74 (~trans(s104, s88)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12074, 11042, 10843])).
% 1.78/1.74 tff(12076,assumption,(~until2p23(s39)), introduced(assumption)).
% 1.78/1.74 tff(12077,assumption,(trans(s104, s39)), introduced(assumption)).
% 1.78/1.74 tff(12078,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12079,plain,
% 1.78/1.74 (((~trans(s104, s39)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s39)) <=> (until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12080,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s39)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12079])).
% 1.78/1.74 tff(12081,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s39)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12080, 12078])).
% 1.78/1.74 tff(12082,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s39)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s39))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12083,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s39) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s39))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12082, 12081])).
% 1.78/1.74 tff(12084,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12083, 10853, 12077, 11532, 12076, 11533])).
% 1.78/1.74 tff(12085,plain,((~trans(s104, s39)) | until2p23(s39) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12086,plain,
% 1.78/1.74 (~trans(s104, s39)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12085, 11554, 10843])).
% 1.78/1.74 tff(12087,assumption,(~until2p23(s57)), introduced(assumption)).
% 1.78/1.74 tff(12088,assumption,(trans(s104, s57)), introduced(assumption)).
% 1.78/1.74 tff(12089,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12090,plain,
% 1.78/1.74 (((~trans(s104, s57)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s57)) <=> (until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12091,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s57)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12090])).
% 1.78/1.74 tff(12092,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s57)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12091, 12089])).
% 1.78/1.74 tff(12093,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s57)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s57))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12094,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s57) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s57))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12093, 12092])).
% 1.78/1.74 tff(12095,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12094, 10853, 12088, 11532, 12087, 11533])).
% 1.78/1.74 tff(12096,plain,((~trans(s104, s57)) | until2p23(s57) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12097,plain,
% 1.78/1.74 (~trans(s104, s57)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12096, 11352, 10843])).
% 1.78/1.74 tff(12098,assumption,(~until2p23(s33)), introduced(assumption)).
% 1.78/1.74 tff(12099,assumption,(trans(s104, s33)), introduced(assumption)).
% 1.78/1.74 tff(12100,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12101,plain,
% 1.78/1.74 (((~trans(s104, s33)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s33)) <=> (until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12102,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s33)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12101])).
% 1.78/1.74 tff(12103,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s33)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12102, 12100])).
% 1.78/1.74 tff(12104,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s33)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s33))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12105,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s33) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s33))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12104, 12103])).
% 1.78/1.74 tff(12106,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12105, 10853, 12099, 11532, 12098, 11533])).
% 1.78/1.74 tff(12107,plain,((~trans(s104, s33)) | until2p23(s33) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12108,plain,
% 1.78/1.74 (~trans(s104, s33)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12107, 11614, 10843])).
% 1.78/1.74 tff(12109,assumption,(~until2p23(s15)), introduced(assumption)).
% 1.78/1.74 tff(12110,assumption,(trans(s104, s15)), introduced(assumption)).
% 1.78/1.74 tff(12111,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12112,plain,
% 1.78/1.74 (((~trans(s104, s15)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s15)) <=> (until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12113,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s15)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12112])).
% 1.78/1.74 tff(12114,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s15)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12113, 12111])).
% 1.78/1.74 tff(12115,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s15)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s15))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12116,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s15) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s15))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12115, 12114])).
% 1.78/1.74 tff(12117,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12116, 10853, 12110, 11532, 12109, 11533])).
% 1.78/1.74 tff(12118,plain,((~trans(s104, s15)) | until2p23(s15) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12119,plain,
% 1.78/1.74 (~trans(s104, s15)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12118, 11926, 10843])).
% 1.78/1.74 tff(12120,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s9, s10)) | until2p23(s10) | (~xuntil2p24(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s9, s10)) | until2p23(s10) | (~xuntil2p24(s9)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12121,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s9, s10)) | until2p23(s10) | (~xuntil2p24(s9)))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12122,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s9, s10)) | until2p23(s10) | (~xuntil2p24(s9))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12121, 12120])).
% 1.78/1.74 tff(12123,plain,
% 1.78/1.74 (until2p23(s10) | (~xuntil2p24(s9))),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12122, 1199, 10882])).
% 1.78/1.74 tff(12124,plain,
% 1.78/1.74 (~xuntil2p24(s9)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12123, 11976])).
% 1.78/1.74 tff(12125,plain,
% 1.78/1.74 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s9) | xuntil2p24(s9) | (~until2p23(s9)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s9) | xuntil2p24(s9) | (~until2p23(s9)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12126,plain,
% 1.78/1.74 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s9) | xuntil2p24(s9) | (~until2p23(s9)))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12127,plain,
% 1.78/1.74 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s9) | xuntil2p24(s9) | (~until2p23(s9))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12126, 12125])).
% 1.78/1.74 tff(12128,plain,
% 1.78/1.74 (xuntil2p24(s9) | (~until2p23(s9))),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12127, 10867, 9335])).
% 1.78/1.74 tff(12129,plain,
% 1.78/1.74 (~until2p23(s9)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12128, 12124])).
% 1.78/1.74 tff(12130,assumption,(~until2p23(s9)), introduced(assumption)).
% 1.78/1.74 tff(12131,assumption,(trans(s104, s9)), introduced(assumption)).
% 1.78/1.74 tff(12132,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12133,plain,
% 1.78/1.74 (((~trans(s104, s9)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s9)) <=> (until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12134,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s9)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12133])).
% 1.78/1.74 tff(12135,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s9)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12134, 12132])).
% 1.78/1.74 tff(12136,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s9)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s9))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12137,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s9) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s9))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12136, 12135])).
% 1.78/1.74 tff(12138,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12137, 10853, 12131, 11532, 12130, 11533])).
% 1.78/1.74 tff(12139,plain,((~trans(s104, s9)) | until2p23(s9) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12140,plain,
% 1.78/1.74 (~trans(s104, s9)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12139, 12129, 10843])).
% 1.78/1.74 tff(12141,assumption,(~until2p23(s62)), introduced(assumption)).
% 1.78/1.74 tff(12142,assumption,(trans(s104, s62)), introduced(assumption)).
% 1.78/1.74 tff(12143,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12144,plain,
% 1.78/1.74 (((~trans(s104, s62)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s62)) <=> (until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12145,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s62)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12144])).
% 1.78/1.74 tff(12146,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s62)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12145, 12143])).
% 1.78/1.74 tff(12147,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s62)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s62))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12148,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s62) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s62))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12147, 12146])).
% 1.78/1.74 tff(12149,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12148, 10853, 12142, 11532, 12141, 11533])).
% 1.78/1.74 tff(12150,plain,((~trans(s104, s62)) | until2p23(s62) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12151,plain,
% 1.78/1.74 (~trans(s104, s62)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12150, 11302, 10843])).
% 1.78/1.74 tff(12152,assumption,(~until2p23(s70)), introduced(assumption)).
% 1.78/1.74 tff(12153,assumption,(trans(s104, s70)), introduced(assumption)).
% 1.78/1.74 tff(12154,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12155,plain,
% 1.78/1.74 (((~trans(s104, s70)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s70)) <=> (until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12156,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s70)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12155])).
% 1.78/1.74 tff(12157,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s70)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12156, 12154])).
% 1.78/1.74 tff(12158,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s70)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s70))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12159,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s70) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s70))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12158, 12157])).
% 1.78/1.74 tff(12160,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12159, 10853, 12153, 11532, 12152, 11533])).
% 1.78/1.74 tff(12161,plain,((~trans(s104, s70)) | until2p23(s70) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12162,plain,
% 1.78/1.74 (~trans(s104, s70)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12161, 11222, 10843])).
% 1.78/1.74 tff(12163,assumption,(~until2p23(s48)), introduced(assumption)).
% 1.78/1.74 tff(12164,assumption,(trans(s104, s48)), introduced(assumption)).
% 1.78/1.74 tff(12165,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12166,plain,
% 1.78/1.74 (((~trans(s104, s48)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s48)) <=> (until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12167,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s48)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12166])).
% 1.78/1.74 tff(12168,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s48)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12167, 12165])).
% 1.78/1.74 tff(12169,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s48)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s48))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12170,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s48) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s48))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12169, 12168])).
% 1.78/1.74 tff(12171,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12170, 10853, 12164, 11532, 12163, 11533])).
% 1.78/1.74 tff(12172,plain,((~trans(s104, s48)) | until2p23(s48) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12173,plain,
% 1.78/1.74 (~trans(s104, s48)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12172, 11442, 10843])).
% 1.78/1.74 tff(12174,assumption,(~until2p23(s13)), introduced(assumption)).
% 1.78/1.74 tff(12175,assumption,(trans(s104, s13)), introduced(assumption)).
% 1.78/1.74 tff(12176,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12177,plain,
% 1.78/1.74 (((~trans(s104, s13)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s13)) <=> (until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12178,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s13)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12177])).
% 1.78/1.74 tff(12179,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s13)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12178, 12176])).
% 1.78/1.74 tff(12180,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s13)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s13))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12181,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s13) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s13))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12180, 12179])).
% 1.78/1.74 tff(12182,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12181, 10853, 12175, 11532, 12174, 11533])).
% 1.78/1.74 tff(12183,plain,((~trans(s104, s13)) | until2p23(s13) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12184,plain,
% 1.78/1.74 (~trans(s104, s13)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12183, 11946, 10843])).
% 1.78/1.74 tff(12185,assumption,(~until2p23(s37)), introduced(assumption)).
% 1.78/1.74 tff(12186,assumption,(trans(s104, s37)), introduced(assumption)).
% 1.78/1.74 tff(12187,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12188,plain,
% 1.78/1.74 (((~trans(s104, s37)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s37)) <=> (until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12189,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s37)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12188])).
% 1.78/1.74 tff(12190,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s37)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12189, 12187])).
% 1.78/1.74 tff(12191,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s37)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s37))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12192,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s37) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s37))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12191, 12190])).
% 1.78/1.74 tff(12193,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12192, 10853, 12186, 11532, 12185, 11533])).
% 1.78/1.74 tff(12194,plain,((~trans(s104, s37)) | until2p23(s37) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12195,plain,
% 1.78/1.74 (~trans(s104, s37)),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12194, 11574, 10843])).
% 1.78/1.74 tff(12196,assumption,(~until2p23(s102)), introduced(assumption)).
% 1.78/1.74 tff(12197,assumption,(trans(s104, s102)), introduced(assumption)).
% 1.78/1.74 tff(12198,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12199,plain,
% 1.78/1.74 (((~trans(s104, s102)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s102)) <=> (until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102)))),
% 1.78/1.74 inference(rewrite,[status(thm)],[])).
% 1.78/1.74 tff(12200,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s102)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102))))),
% 1.78/1.74 inference(monotonicity,[status(thm)],[12199])).
% 1.78/1.74 tff(12201,plain,
% 1.78/1.74 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s102)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102)))),
% 1.78/1.74 inference(transitivity,[status(thm)],[12200, 12198])).
% 1.78/1.74 tff(12202,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s102)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s102))),
% 1.78/1.74 inference(quant_inst,[status(thm)],[])).
% 1.78/1.74 tff(12203,plain,
% 1.78/1.74 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s102) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s102))),
% 1.78/1.74 inference(modus_ponens,[status(thm)],[12202, 12201])).
% 1.78/1.74 tff(12204,plain,
% 1.78/1.74 ($false),
% 1.78/1.74 inference(unit_resolution,[status(thm)],[12203, 10853, 12197, 11532, 12196, 11533])).
% 1.78/1.74 tff(12205,plain,((~trans(s104, s102)) | until2p23(s102) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.74 tff(12206,plain,
% 1.78/1.75 (~trans(s104, s102)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12205, 10902, 10843])).
% 1.78/1.75 tff(12207,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s8, s9)) | until2p23(s9) | (~xuntil2p24(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s8, s9)) | until2p23(s9) | (~xuntil2p24(s8)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12208,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s8, s9)) | until2p23(s9) | (~xuntil2p24(s8)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12209,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s8, s9)) | until2p23(s9) | (~xuntil2p24(s8))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12208, 12207])).
% 1.78/1.75 tff(12210,plain,
% 1.78/1.75 (until2p23(s9) | (~xuntil2p24(s8))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12209, 1132, 10882])).
% 1.78/1.75 tff(12211,plain,
% 1.78/1.75 (~xuntil2p24(s8)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12210, 12129])).
% 1.78/1.75 tff(12212,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s8) | xuntil2p24(s8) | (~until2p23(s8)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s8) | xuntil2p24(s8) | (~until2p23(s8)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12213,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s8) | xuntil2p24(s8) | (~until2p23(s8)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12214,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s8) | xuntil2p24(s8) | (~until2p23(s8))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12213, 12212])).
% 1.78/1.75 tff(12215,plain,
% 1.78/1.75 (xuntil2p24(s8) | (~until2p23(s8))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12214, 10867, 9344])).
% 1.78/1.75 tff(12216,plain,
% 1.78/1.75 (~until2p23(s8)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12215, 12211])).
% 1.78/1.75 tff(12217,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s7, s8)) | until2p23(s8) | (~xuntil2p24(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s7, s8)) | until2p23(s8) | (~xuntil2p24(s7)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12218,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s7, s8)) | until2p23(s8) | (~xuntil2p24(s7)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12219,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s7, s8)) | until2p23(s8) | (~xuntil2p24(s7))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12218, 12217])).
% 1.78/1.75 tff(12220,plain,
% 1.78/1.75 (until2p23(s8) | (~xuntil2p24(s7))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12219, 1043, 10882])).
% 1.78/1.75 tff(12221,plain,
% 1.78/1.75 (~xuntil2p24(s7)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12220, 12216])).
% 1.78/1.75 tff(12222,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s7) | xuntil2p24(s7) | (~until2p23(s7)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s7) | xuntil2p24(s7) | (~until2p23(s7)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12223,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s7) | xuntil2p24(s7) | (~until2p23(s7)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12224,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s7) | xuntil2p24(s7) | (~until2p23(s7))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12223, 12222])).
% 1.78/1.75 tff(12225,plain,
% 1.78/1.75 (xuntil2p24(s7) | (~until2p23(s7))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12224, 10867, 9352])).
% 1.78/1.75 tff(12226,plain,
% 1.78/1.75 (~until2p23(s7)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12225, 12221])).
% 1.78/1.75 tff(12227,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s6, s7)) | until2p23(s7) | (~xuntil2p24(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s6, s7)) | until2p23(s7) | (~xuntil2p24(s6)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12228,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s6, s7)) | until2p23(s7) | (~xuntil2p24(s6)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12229,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s6, s7)) | until2p23(s7) | (~xuntil2p24(s6))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12228, 12227])).
% 1.78/1.75 tff(12230,plain,
% 1.78/1.75 (until2p23(s7) | (~xuntil2p24(s6))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12229, 958, 10882])).
% 1.78/1.75 tff(12231,plain,
% 1.78/1.75 (~xuntil2p24(s6)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12230, 12226])).
% 1.78/1.75 tff(12232,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s6) | xuntil2p24(s6) | (~until2p23(s6)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s6) | xuntil2p24(s6) | (~until2p23(s6)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12233,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s6) | xuntil2p24(s6) | (~until2p23(s6)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12234,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s6) | xuntil2p24(s6) | (~until2p23(s6))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12233, 12232])).
% 1.78/1.75 tff(12235,plain,
% 1.78/1.75 (xuntil2p24(s6) | (~until2p23(s6))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12234, 10867, 9511])).
% 1.78/1.75 tff(12236,plain,
% 1.78/1.75 (~until2p23(s6)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12235, 12231])).
% 1.78/1.75 tff(12237,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s5, s6)) | until2p23(s6) | (~xuntil2p24(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s5, s6)) | until2p23(s6) | (~xuntil2p24(s5)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12238,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s5, s6)) | until2p23(s6) | (~xuntil2p24(s5)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12239,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s5, s6)) | until2p23(s6) | (~xuntil2p24(s5))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12238, 12237])).
% 1.78/1.75 tff(12240,plain,
% 1.78/1.75 (until2p23(s6) | (~xuntil2p24(s5))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12239, 874, 10882])).
% 1.78/1.75 tff(12241,plain,
% 1.78/1.75 (~xuntil2p24(s5)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12240, 12236])).
% 1.78/1.75 tff(12242,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s5) | xuntil2p24(s5) | (~until2p23(s5)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s5) | xuntil2p24(s5) | (~until2p23(s5)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12243,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s5) | xuntil2p24(s5) | (~until2p23(s5)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12244,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s5) | xuntil2p24(s5) | (~until2p23(s5))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12243, 12242])).
% 1.78/1.75 tff(12245,plain,
% 1.78/1.75 (xuntil2p24(s5) | (~until2p23(s5))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12244, 10867, 9368])).
% 1.78/1.75 tff(12246,plain,
% 1.78/1.75 (~until2p23(s5)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12245, 12241])).
% 1.78/1.75 tff(12247,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s4, s5)) | until2p23(s5) | (~xuntil2p24(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s4, s5)) | until2p23(s5) | (~xuntil2p24(s4)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12248,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s4, s5)) | until2p23(s5) | (~xuntil2p24(s4)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12249,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s4, s5)) | until2p23(s5) | (~xuntil2p24(s4))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12248, 12247])).
% 1.78/1.75 tff(12250,plain,
% 1.78/1.75 (until2p23(s5) | (~xuntil2p24(s4))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12249, 708, 10882])).
% 1.78/1.75 tff(12251,plain,
% 1.78/1.75 (~xuntil2p24(s4)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12250, 12246])).
% 1.78/1.75 tff(12252,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s4) | xuntil2p24(s4) | (~until2p23(s4)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s4) | xuntil2p24(s4) | (~until2p23(s4)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12253,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s4) | xuntil2p24(s4) | (~until2p23(s4)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12254,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s4) | xuntil2p24(s4) | (~until2p23(s4))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12253, 12252])).
% 1.78/1.75 tff(12255,plain,
% 1.78/1.75 (xuntil2p24(s4) | (~until2p23(s4))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12254, 10867, 9377])).
% 1.78/1.75 tff(12256,plain,
% 1.78/1.75 (~until2p23(s4)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12255, 12251])).
% 1.78/1.75 tff(12257,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s3, s4)) | until2p23(s4) | (~xuntil2p24(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s3, s4)) | until2p23(s4) | (~xuntil2p24(s3)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12258,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s3, s4)) | until2p23(s4) | (~xuntil2p24(s3)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12259,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s3, s4)) | until2p23(s4) | (~xuntil2p24(s3))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12258, 12257])).
% 1.78/1.75 tff(12260,plain,
% 1.78/1.75 (until2p23(s4) | (~xuntil2p24(s3))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12259, 599, 10882])).
% 1.78/1.75 tff(12261,plain,
% 1.78/1.75 (~xuntil2p24(s3)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12260, 12256])).
% 1.78/1.75 tff(12262,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s3) | xuntil2p24(s3) | (~until2p23(s3)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s3) | xuntil2p24(s3) | (~until2p23(s3)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12263,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s3) | xuntil2p24(s3) | (~until2p23(s3)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12264,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s3) | xuntil2p24(s3) | (~until2p23(s3))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12263, 12262])).
% 1.78/1.75 tff(12265,plain,
% 1.78/1.75 (xuntil2p24(s3) | (~until2p23(s3))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12264, 10867, 9385])).
% 1.78/1.75 tff(12266,plain,
% 1.78/1.75 (~until2p23(s3)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12265, 12261])).
% 1.78/1.75 tff(12267,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s2, s3)) | until2p23(s3) | (~xuntil2p24(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s2, s3)) | until2p23(s3) | (~xuntil2p24(s2)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12268,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s2, s3)) | until2p23(s3) | (~xuntil2p24(s2)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12269,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s2, s3)) | until2p23(s3) | (~xuntil2p24(s2))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12268, 12267])).
% 1.78/1.75 tff(12270,plain,
% 1.78/1.75 (until2p23(s3) | (~xuntil2p24(s2))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12269, 480, 10882])).
% 1.78/1.75 tff(12271,plain,
% 1.78/1.75 (~xuntil2p24(s2)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12270, 12266])).
% 1.78/1.75 tff(12272,plain,
% 1.78/1.75 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s2) | xuntil2p24(s2) | (~until2p23(s2)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s2) | xuntil2p24(s2) | (~until2p23(s2)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12273,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s2) | xuntil2p24(s2) | (~until2p23(s2)))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12274,plain,
% 1.78/1.75 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s2) | xuntil2p24(s2) | (~until2p23(s2))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12273, 12272])).
% 1.78/1.75 tff(12275,plain,
% 1.78/1.75 (xuntil2p24(s2) | (~until2p23(s2))),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12274, 10867, 9396])).
% 1.78/1.75 tff(12276,plain,
% 1.78/1.75 (~until2p23(s2)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12275, 12271])).
% 1.78/1.75 tff(12277,assumption,(~until2p23(s2)), introduced(assumption)).
% 1.78/1.75 tff(12278,assumption,(trans(s104, s2)), introduced(assumption)).
% 1.78/1.75 tff(12279,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12280,plain,
% 1.78/1.75 (((~trans(s104, s2)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s2)) <=> (until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12281,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s2)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12280])).
% 1.78/1.75 tff(12282,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s2)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12281, 12279])).
% 1.78/1.75 tff(12283,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s2)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s2))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12284,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s2) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s2))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12283, 12282])).
% 1.78/1.75 tff(12285,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12284, 10853, 12278, 11532, 12277, 11533])).
% 1.78/1.75 tff(12286,plain,((~trans(s104, s2)) | until2p23(s2) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12287,plain,
% 1.78/1.75 (~trans(s104, s2)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12286, 12276, 10843])).
% 1.78/1.75 tff(12288,assumption,(~until2p23(s52)), introduced(assumption)).
% 1.78/1.75 tff(12289,assumption,(trans(s104, s52)), introduced(assumption)).
% 1.78/1.75 tff(12290,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12291,plain,
% 1.78/1.75 (((~trans(s104, s52)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s52)) <=> (until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12292,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s52)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12291])).
% 1.78/1.75 tff(12293,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s52)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12292, 12290])).
% 1.78/1.75 tff(12294,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s52)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s52))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12295,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s52) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s52))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12294, 12293])).
% 1.78/1.75 tff(12296,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12295, 10853, 12289, 11532, 12288, 11533])).
% 1.78/1.75 tff(12297,plain,((~trans(s104, s52)) | until2p23(s52) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12298,plain,
% 1.78/1.75 (~trans(s104, s52)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12297, 11402, 10843])).
% 1.78/1.75 tff(12299,assumption,(~until2p23(s29)), introduced(assumption)).
% 1.78/1.75 tff(12300,assumption,(trans(s104, s29)), introduced(assumption)).
% 1.78/1.75 tff(12301,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12302,plain,
% 1.78/1.75 (((~trans(s104, s29)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s29)) <=> (until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12303,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s29)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12302])).
% 1.78/1.75 tff(12304,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s29)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12303, 12301])).
% 1.78/1.75 tff(12305,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s29)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s29))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12306,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s29) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s29))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12305, 12304])).
% 1.78/1.75 tff(12307,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12306, 10853, 12300, 11532, 12299, 11533])).
% 1.78/1.75 tff(12308,plain,((~trans(s104, s29)) | until2p23(s29) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12309,plain,
% 1.78/1.75 (~trans(s104, s29)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12308, 11665, 10843])).
% 1.78/1.75 tff(12310,assumption,(~until2p23(s31)), introduced(assumption)).
% 1.78/1.75 tff(12311,assumption,(trans(s104, s31)), introduced(assumption)).
% 1.78/1.75 tff(12312,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12313,plain,
% 1.78/1.75 (((~trans(s104, s31)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s31)) <=> (until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12314,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s31)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12313])).
% 1.78/1.75 tff(12315,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s31)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12314, 12312])).
% 1.78/1.75 tff(12316,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s31)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s31))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12317,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s31) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s31))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12316, 12315])).
% 1.78/1.75 tff(12318,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12317, 10853, 12311, 11532, 12310, 11533])).
% 1.78/1.75 tff(12319,plain,((~trans(s104, s31)) | until2p23(s31) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12320,plain,
% 1.78/1.75 (~trans(s104, s31)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12319, 11645, 10843])).
% 1.78/1.75 tff(12321,assumption,(~until2p23(s55)), introduced(assumption)).
% 1.78/1.75 tff(12322,assumption,(trans(s104, s55)), introduced(assumption)).
% 1.78/1.75 tff(12323,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12324,plain,
% 1.78/1.75 (((~trans(s104, s55)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s55)) <=> (until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12325,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s55)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12324])).
% 1.78/1.75 tff(12326,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s55)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12325, 12323])).
% 1.78/1.75 tff(12327,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s55)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s55))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12328,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s55) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s55))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12327, 12326])).
% 1.78/1.75 tff(12329,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12328, 10853, 12322, 11532, 12321, 11533])).
% 1.78/1.75 tff(12330,plain,((~trans(s104, s55)) | until2p23(s55) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12331,plain,
% 1.78/1.75 (~trans(s104, s55)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12330, 11372, 10843])).
% 1.78/1.75 tff(12332,assumption,(~until2p23(s7)), introduced(assumption)).
% 1.78/1.75 tff(12333,assumption,(trans(s104, s7)), introduced(assumption)).
% 1.78/1.75 tff(12334,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12335,plain,
% 1.78/1.75 (((~trans(s104, s7)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s7)) <=> (until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12336,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s7)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12335])).
% 1.78/1.75 tff(12337,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s7)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7)))),
% 1.78/1.75 inference(transitivity,[status(thm)],[12336, 12334])).
% 1.78/1.75 tff(12338,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s7)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s7))),
% 1.78/1.75 inference(quant_inst,[status(thm)],[])).
% 1.78/1.75 tff(12339,plain,
% 1.78/1.75 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s7) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s7))),
% 1.78/1.75 inference(modus_ponens,[status(thm)],[12338, 12337])).
% 1.78/1.75 tff(12340,plain,
% 1.78/1.75 ($false),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12339, 10853, 12333, 11532, 12332, 11533])).
% 1.78/1.75 tff(12341,plain,((~trans(s104, s7)) | until2p23(s7) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.75 tff(12342,plain,
% 1.78/1.75 (~trans(s104, s7)),
% 1.78/1.75 inference(unit_resolution,[status(thm)],[12341, 12226, 10843])).
% 1.78/1.75 tff(12343,assumption,(~until2p23(s64)), introduced(assumption)).
% 1.78/1.75 tff(12344,assumption,(trans(s104, s64)), introduced(assumption)).
% 1.78/1.75 tff(12345,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12346,plain,
% 1.78/1.75 (((~trans(s104, s64)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s64)) <=> (until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64)))),
% 1.78/1.75 inference(rewrite,[status(thm)],[])).
% 1.78/1.75 tff(12347,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s64)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64))))),
% 1.78/1.75 inference(monotonicity,[status(thm)],[12346])).
% 1.78/1.75 tff(12348,plain,
% 1.78/1.75 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s64)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12347, 12345])).
% 1.78/1.76 tff(12349,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s64)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s64))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12350,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s64) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s64))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12349, 12348])).
% 1.78/1.76 tff(12351,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12350, 10853, 12344, 11532, 12343, 11533])).
% 1.78/1.76 tff(12352,plain,((~trans(s104, s64)) | until2p23(s64) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12353,plain,
% 1.78/1.76 (~trans(s104, s64)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12352, 11282, 10843])).
% 1.78/1.76 tff(12354,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s1, s2)) | until2p23(s2) | (~xuntil2p24(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s1, s2)) | until2p23(s2) | (~xuntil2p24(s1)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12355,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s1, s2)) | until2p23(s2) | (~xuntil2p24(s1)))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12356,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s1, s2)) | until2p23(s2) | (~xuntil2p24(s1))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12355, 12354])).
% 1.78/1.76 tff(12357,plain,
% 1.78/1.76 (until2p23(s2) | (~xuntil2p24(s1))),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12356, 278, 10882])).
% 1.78/1.76 tff(12358,plain,
% 1.78/1.76 (~xuntil2p24(s1)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12357, 12276])).
% 1.78/1.76 tff(12359,plain,
% 1.78/1.76 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s1) | xuntil2p24(s1) | (~until2p23(s1)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s1) | xuntil2p24(s1) | (~until2p23(s1)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12360,plain,
% 1.78/1.76 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s1) | xuntil2p24(s1) | (~until2p23(s1)))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12361,plain,
% 1.78/1.76 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s1) | xuntil2p24(s1) | (~until2p23(s1))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12360, 12359])).
% 1.78/1.76 tff(12362,plain,
% 1.78/1.76 (xuntil2p24(s1) | (~until2p23(s1))),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12361, 10867, 9405])).
% 1.78/1.76 tff(12363,plain,
% 1.78/1.76 (~until2p23(s1)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12362, 12358])).
% 1.78/1.76 tff(12364,assumption,(~until2p23(s1)), introduced(assumption)).
% 1.78/1.76 tff(12365,assumption,(trans(s104, s1)), introduced(assumption)).
% 1.78/1.76 tff(12366,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12367,plain,
% 1.78/1.76 (((~trans(s104, s1)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s1)) <=> (until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12368,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s1)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12367])).
% 1.78/1.76 tff(12369,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s1)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12368, 12366])).
% 1.78/1.76 tff(12370,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s1)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s1))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12371,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s1) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s1))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12370, 12369])).
% 1.78/1.76 tff(12372,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12371, 10853, 12365, 11532, 12364, 11533])).
% 1.78/1.76 tff(12373,plain,((~trans(s104, s1)) | until2p23(s1) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12374,plain,
% 1.78/1.76 (~trans(s104, s1)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12373, 12363, 10843])).
% 1.78/1.76 tff(12375,assumption,(~until2p23(s99)), introduced(assumption)).
% 1.78/1.76 tff(12376,assumption,(trans(s104, s99)), introduced(assumption)).
% 1.78/1.76 tff(12377,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12378,plain,
% 1.78/1.76 (((~trans(s104, s99)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s99)) <=> (until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12379,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s99)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12378])).
% 1.78/1.76 tff(12380,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s99)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12379, 12377])).
% 1.78/1.76 tff(12381,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s99)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s99))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12382,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s99) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s99))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12381, 12380])).
% 1.78/1.76 tff(12383,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12382, 10853, 12376, 11532, 12375, 11533])).
% 1.78/1.76 tff(12384,plain,((~trans(s104, s99)) | until2p23(s99) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12385,plain,
% 1.78/1.76 (~trans(s104, s99)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12384, 10932, 10843])).
% 1.78/1.76 tff(12386,assumption,(~until2p23(s63)), introduced(assumption)).
% 1.78/1.76 tff(12387,assumption,(trans(s104, s63)), introduced(assumption)).
% 1.78/1.76 tff(12388,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12389,plain,
% 1.78/1.76 (((~trans(s104, s63)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s63)) <=> (until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12390,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s63)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12389])).
% 1.78/1.76 tff(12391,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s63)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12390, 12388])).
% 1.78/1.76 tff(12392,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s63)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s63))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12393,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s63) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s63))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12392, 12391])).
% 1.78/1.76 tff(12394,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12393, 10853, 12387, 11532, 12386, 11533])).
% 1.78/1.76 tff(12395,plain,((~trans(s104, s63)) | until2p23(s63) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12396,plain,
% 1.78/1.76 (~trans(s104, s63)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12395, 11292, 10843])).
% 1.78/1.76 tff(12397,assumption,(~until2p23(s25)), introduced(assumption)).
% 1.78/1.76 tff(12398,assumption,(trans(s104, s25)), introduced(assumption)).
% 1.78/1.76 tff(12399,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12400,plain,
% 1.78/1.76 (((~trans(s104, s25)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s25)) <=> (until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12401,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s25)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12400])).
% 1.78/1.76 tff(12402,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s25)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12401, 12399])).
% 1.78/1.76 tff(12403,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s25)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s25))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12404,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s25) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s25))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12403, 12402])).
% 1.78/1.76 tff(12405,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12404, 10853, 12398, 11532, 12397, 11533])).
% 1.78/1.76 tff(12406,plain,((~trans(s104, s25)) | until2p23(s25) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12407,plain,
% 1.78/1.76 (~trans(s104, s25)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12406, 11705, 10843])).
% 1.78/1.76 tff(12408,assumption,(~until2p23(s73)), introduced(assumption)).
% 1.78/1.76 tff(12409,assumption,(trans(s104, s73)), introduced(assumption)).
% 1.78/1.76 tff(12410,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12411,plain,
% 1.78/1.76 (((~trans(s104, s73)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s73)) <=> (until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12412,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s73)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12411])).
% 1.78/1.76 tff(12413,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s73)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12412, 12410])).
% 1.78/1.76 tff(12414,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s73)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s73))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12415,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s73) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s73))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12414, 12413])).
% 1.78/1.76 tff(12416,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12415, 10853, 12409, 11532, 12408, 11533])).
% 1.78/1.76 tff(12417,plain,((~trans(s104, s73)) | until2p23(s73) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12418,plain,
% 1.78/1.76 (~trans(s104, s73)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12417, 11192, 10843])).
% 1.78/1.76 tff(12419,assumption,(~until2p23(s12)), introduced(assumption)).
% 1.78/1.76 tff(12420,assumption,(trans(s104, s12)), introduced(assumption)).
% 1.78/1.76 tff(12421,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12422,plain,
% 1.78/1.76 (((~trans(s104, s12)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s12)) <=> (until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12423,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s12)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12422])).
% 1.78/1.76 tff(12424,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s12)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12423, 12421])).
% 1.78/1.76 tff(12425,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s12)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s12))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12426,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s12) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s12))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12425, 12424])).
% 1.78/1.76 tff(12427,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12426, 10853, 12420, 11532, 12419, 11533])).
% 1.78/1.76 tff(12428,plain,((~trans(s104, s12)) | until2p23(s12) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12429,plain,
% 1.78/1.76 (~trans(s104, s12)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12428, 11956, 10843])).
% 1.78/1.76 tff(12430,assumption,(~until2p23(s21)), introduced(assumption)).
% 1.78/1.76 tff(12431,assumption,(trans(s104, s21)), introduced(assumption)).
% 1.78/1.76 tff(12432,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12433,plain,
% 1.78/1.76 (((~trans(s104, s21)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s21)) <=> (until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12434,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s21)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12433])).
% 1.78/1.76 tff(12435,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s21)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12434, 12432])).
% 1.78/1.76 tff(12436,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s21)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s21))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12437,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s21) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s21))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12436, 12435])).
% 1.78/1.76 tff(12438,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12437, 10853, 12431, 11532, 12430, 11533])).
% 1.78/1.76 tff(12439,plain,((~trans(s104, s21)) | until2p23(s21) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12440,plain,
% 1.78/1.76 (~trans(s104, s21)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12439, 11767, 10843])).
% 1.78/1.76 tff(12441,assumption,(~until2p23(s93)), introduced(assumption)).
% 1.78/1.76 tff(12442,assumption,(trans(s104, s93)), introduced(assumption)).
% 1.78/1.76 tff(12443,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12444,plain,
% 1.78/1.76 (((~trans(s104, s93)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s93)) <=> (until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12445,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s93)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12444])).
% 1.78/1.76 tff(12446,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s93)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12445, 12443])).
% 1.78/1.76 tff(12447,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s93)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s93))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12448,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s93) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s93))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12447, 12446])).
% 1.78/1.76 tff(12449,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12448, 10853, 12442, 11532, 12441, 11533])).
% 1.78/1.76 tff(12450,plain,((~trans(s104, s93)) | until2p23(s93) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12451,plain,
% 1.78/1.76 (~trans(s104, s93)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12450, 10992, 10843])).
% 1.78/1.76 tff(12452,assumption,(~until2p23(s80)), introduced(assumption)).
% 1.78/1.76 tff(12453,assumption,(trans(s104, s80)), introduced(assumption)).
% 1.78/1.76 tff(12454,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12455,plain,
% 1.78/1.76 (((~trans(s104, s80)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s80)) <=> (until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12456,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s80)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12455])).
% 1.78/1.76 tff(12457,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s80)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12456, 12454])).
% 1.78/1.76 tff(12458,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s80)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s80))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12459,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s80) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s80))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12458, 12457])).
% 1.78/1.76 tff(12460,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12459, 10853, 12453, 11532, 12452, 11533])).
% 1.78/1.76 tff(12461,plain,((~trans(s104, s80)) | until2p23(s80) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12462,plain,
% 1.78/1.76 (~trans(s104, s80)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12461, 11122, 10843])).
% 1.78/1.76 tff(12463,assumption,(~until2p23(s28)), introduced(assumption)).
% 1.78/1.76 tff(12464,assumption,(trans(s104, s28)), introduced(assumption)).
% 1.78/1.76 tff(12465,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12466,plain,
% 1.78/1.76 (((~trans(s104, s28)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s28)) <=> (until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12467,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s28)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12466])).
% 1.78/1.76 tff(12468,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s28)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12467, 12465])).
% 1.78/1.76 tff(12469,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s28)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s28))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12470,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s28) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s28))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12469, 12468])).
% 1.78/1.76 tff(12471,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12470, 10853, 12464, 11532, 12463, 11533])).
% 1.78/1.76 tff(12472,plain,((~trans(s104, s28)) | until2p23(s28) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12473,plain,
% 1.78/1.76 (~trans(s104, s28)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12472, 11675, 10843])).
% 1.78/1.76 tff(12474,assumption,(~until2p23(s56)), introduced(assumption)).
% 1.78/1.76 tff(12475,assumption,(trans(s104, s56)), introduced(assumption)).
% 1.78/1.76 tff(12476,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12477,plain,
% 1.78/1.76 (((~trans(s104, s56)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s56)) <=> (until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12478,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s56)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56))))),
% 1.78/1.76 inference(monotonicity,[status(thm)],[12477])).
% 1.78/1.76 tff(12479,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s56)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56)))),
% 1.78/1.76 inference(transitivity,[status(thm)],[12478, 12476])).
% 1.78/1.76 tff(12480,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s56)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s56))),
% 1.78/1.76 inference(quant_inst,[status(thm)],[])).
% 1.78/1.76 tff(12481,plain,
% 1.78/1.76 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s56) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s56))),
% 1.78/1.76 inference(modus_ponens,[status(thm)],[12480, 12479])).
% 1.78/1.76 tff(12482,plain,
% 1.78/1.76 ($false),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12481, 10853, 12475, 11532, 12474, 11533])).
% 1.78/1.76 tff(12483,plain,((~trans(s104, s56)) | until2p23(s56) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.76 tff(12484,plain,
% 1.78/1.76 (~trans(s104, s56)),
% 1.78/1.76 inference(unit_resolution,[status(thm)],[12483, 11362, 10843])).
% 1.78/1.76 tff(12485,assumption,(~until2p23(s27)), introduced(assumption)).
% 1.78/1.76 tff(12486,assumption,(trans(s104, s27)), introduced(assumption)).
% 1.78/1.76 tff(12487,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12488,plain,
% 1.78/1.76 (((~trans(s104, s27)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s27)) <=> (until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27)))),
% 1.78/1.76 inference(rewrite,[status(thm)],[])).
% 1.78/1.76 tff(12489,plain,
% 1.78/1.76 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s27)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12488])).
% 1.78/1.77 tff(12490,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s27)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12489, 12487])).
% 1.78/1.77 tff(12491,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s27)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s27))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12492,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s27) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s27))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12491, 12490])).
% 1.78/1.77 tff(12493,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12492, 10853, 12486, 11532, 12485, 11533])).
% 1.78/1.77 tff(12494,plain,((~trans(s104, s27)) | until2p23(s27) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12495,plain,
% 1.78/1.77 (~trans(s104, s27)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12494, 11685, 10843])).
% 1.78/1.77 tff(12496,assumption,(~until2p23(s75)), introduced(assumption)).
% 1.78/1.77 tff(12497,assumption,(trans(s104, s75)), introduced(assumption)).
% 1.78/1.77 tff(12498,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12499,plain,
% 1.78/1.77 (((~trans(s104, s75)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s75)) <=> (until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12500,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s75)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12499])).
% 1.78/1.77 tff(12501,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s75)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12500, 12498])).
% 1.78/1.77 tff(12502,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s75)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s75))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12503,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s75) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s75))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12502, 12501])).
% 1.78/1.77 tff(12504,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12503, 10853, 12497, 11532, 12496, 11533])).
% 1.78/1.77 tff(12505,plain,((~trans(s104, s75)) | until2p23(s75) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12506,plain,
% 1.78/1.77 (~trans(s104, s75)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12505, 11172, 10843])).
% 1.78/1.77 tff(12507,assumption,(~until2p23(s76)), introduced(assumption)).
% 1.78/1.77 tff(12508,assumption,(trans(s104, s76)), introduced(assumption)).
% 1.78/1.77 tff(12509,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12510,plain,
% 1.78/1.77 (((~trans(s104, s76)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s76)) <=> (until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12511,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s76)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12510])).
% 1.78/1.77 tff(12512,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s76)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12511, 12509])).
% 1.78/1.77 tff(12513,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s76)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s76))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12514,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s76) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s76))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12513, 12512])).
% 1.78/1.77 tff(12515,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12514, 10853, 12508, 11532, 12507, 11533])).
% 1.78/1.77 tff(12516,plain,((~trans(s104, s76)) | until2p23(s76) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12517,plain,
% 1.78/1.77 (~trans(s104, s76)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12516, 11162, 10843])).
% 1.78/1.77 tff(12518,assumption,(~until2p23(s69)), introduced(assumption)).
% 1.78/1.77 tff(12519,assumption,(trans(s104, s69)), introduced(assumption)).
% 1.78/1.77 tff(12520,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12521,plain,
% 1.78/1.77 (((~trans(s104, s69)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s69)) <=> (until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12522,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s69)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12521])).
% 1.78/1.77 tff(12523,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s69)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12522, 12520])).
% 1.78/1.77 tff(12524,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s69)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s69))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12525,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s69) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s69))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12524, 12523])).
% 1.78/1.77 tff(12526,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12525, 10853, 12519, 11532, 12518, 11533])).
% 1.78/1.77 tff(12527,plain,((~trans(s104, s69)) | until2p23(s69) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12528,plain,
% 1.78/1.77 (~trans(s104, s69)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12527, 11232, 10843])).
% 1.78/1.77 tff(12529,assumption,(~until2p23(s5)), introduced(assumption)).
% 1.78/1.77 tff(12530,assumption,(trans(s104, s5)), introduced(assumption)).
% 1.78/1.77 tff(12531,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12532,plain,
% 1.78/1.77 (((~trans(s104, s5)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s5)) <=> (until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12533,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s5)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12532])).
% 1.78/1.77 tff(12534,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s5)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12533, 12531])).
% 1.78/1.77 tff(12535,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s5)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s5))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12536,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s5) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s5))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12535, 12534])).
% 1.78/1.77 tff(12537,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12536, 10853, 12530, 11532, 12529, 11533])).
% 1.78/1.77 tff(12538,plain,((~trans(s104, s5)) | until2p23(s5) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12539,plain,
% 1.78/1.77 (~trans(s104, s5)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12538, 12246, 10843])).
% 1.78/1.77 tff(12540,assumption,(~until2p23(s51)), introduced(assumption)).
% 1.78/1.77 tff(12541,assumption,(trans(s104, s51)), introduced(assumption)).
% 1.78/1.77 tff(12542,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12543,plain,
% 1.78/1.77 (((~trans(s104, s51)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s51)) <=> (until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12544,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s51)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12543])).
% 1.78/1.77 tff(12545,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s51)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12544, 12542])).
% 1.78/1.77 tff(12546,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s51)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s51))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12547,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s51) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s51))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12546, 12545])).
% 1.78/1.77 tff(12548,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12547, 10853, 12541, 11532, 12540, 11533])).
% 1.78/1.77 tff(12549,plain,((~trans(s104, s51)) | until2p23(s51) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12550,plain,
% 1.78/1.77 (~trans(s104, s51)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12549, 11412, 10843])).
% 1.78/1.77 tff(12551,assumption,(~until2p23(s58)), introduced(assumption)).
% 1.78/1.77 tff(12552,assumption,(trans(s104, s58)), introduced(assumption)).
% 1.78/1.77 tff(12553,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12554,plain,
% 1.78/1.77 (((~trans(s104, s58)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s58)) <=> (until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12555,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s58)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12554])).
% 1.78/1.77 tff(12556,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s58)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12555, 12553])).
% 1.78/1.77 tff(12557,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s58)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s58))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12558,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s58) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s58))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12557, 12556])).
% 1.78/1.77 tff(12559,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12558, 10853, 12552, 11532, 12551, 11533])).
% 1.78/1.77 tff(12560,plain,((~trans(s104, s58)) | until2p23(s58) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12561,plain,
% 1.78/1.77 (~trans(s104, s58)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12560, 11342, 10843])).
% 1.78/1.77 tff(12562,assumption,(~until2p23(s49)), introduced(assumption)).
% 1.78/1.77 tff(12563,assumption,(trans(s104, s49)), introduced(assumption)).
% 1.78/1.77 tff(12564,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12565,plain,
% 1.78/1.77 (((~trans(s104, s49)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s49)) <=> (until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12566,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s49)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12565])).
% 1.78/1.77 tff(12567,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s49)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12566, 12564])).
% 1.78/1.77 tff(12568,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s49)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s49))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12569,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s49) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s49))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12568, 12567])).
% 1.78/1.77 tff(12570,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12569, 10853, 12563, 11532, 12562, 11533])).
% 1.78/1.77 tff(12571,plain,((~trans(s104, s49)) | until2p23(s49) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12572,plain,
% 1.78/1.77 (~trans(s104, s49)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12571, 11432, 10843])).
% 1.78/1.77 tff(12573,assumption,(~until2p23(s59)), introduced(assumption)).
% 1.78/1.77 tff(12574,assumption,(trans(s104, s59)), introduced(assumption)).
% 1.78/1.77 tff(12575,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12576,plain,
% 1.78/1.77 (((~trans(s104, s59)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s59)) <=> (until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12577,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s59)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12576])).
% 1.78/1.77 tff(12578,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s59)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12577, 12575])).
% 1.78/1.77 tff(12579,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s59)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s59))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12580,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s59) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s59))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12579, 12578])).
% 1.78/1.77 tff(12581,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12580, 10853, 12574, 11532, 12573, 11533])).
% 1.78/1.77 tff(12582,plain,((~trans(s104, s59)) | until2p23(s59) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12583,plain,
% 1.78/1.77 (~trans(s104, s59)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12582, 11332, 10843])).
% 1.78/1.77 tff(12584,assumption,(~until2p23(s60)), introduced(assumption)).
% 1.78/1.77 tff(12585,assumption,(trans(s104, s60)), introduced(assumption)).
% 1.78/1.77 tff(12586,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12587,plain,
% 1.78/1.77 (((~trans(s104, s60)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s60)) <=> (until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12588,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s60)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12587])).
% 1.78/1.77 tff(12589,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s60)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12588, 12586])).
% 1.78/1.77 tff(12590,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s60)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s60))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12591,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s60) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s60))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12590, 12589])).
% 1.78/1.77 tff(12592,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12591, 10853, 12585, 11532, 12584, 11533])).
% 1.78/1.77 tff(12593,plain,((~trans(s104, s60)) | until2p23(s60) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12594,plain,
% 1.78/1.77 (~trans(s104, s60)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12593, 11322, 10843])).
% 1.78/1.77 tff(12595,assumption,(~until2p23(s53)), introduced(assumption)).
% 1.78/1.77 tff(12596,assumption,(trans(s104, s53)), introduced(assumption)).
% 1.78/1.77 tff(12597,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12598,plain,
% 1.78/1.77 (((~trans(s104, s53)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s53)) <=> (until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12599,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s53)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12598])).
% 1.78/1.77 tff(12600,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s53)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12599, 12597])).
% 1.78/1.77 tff(12601,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s53)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s53))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12602,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s53) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s53))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12601, 12600])).
% 1.78/1.77 tff(12603,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12602, 10853, 12596, 11532, 12595, 11533])).
% 1.78/1.77 tff(12604,plain,((~trans(s104, s53)) | until2p23(s53) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12605,plain,
% 1.78/1.77 (~trans(s104, s53)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12604, 11392, 10843])).
% 1.78/1.77 tff(12606,assumption,(~until2p23(s8)), introduced(assumption)).
% 1.78/1.77 tff(12607,assumption,(trans(s104, s8)), introduced(assumption)).
% 1.78/1.77 tff(12608,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12609,plain,
% 1.78/1.77 (((~trans(s104, s8)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s8)) <=> (until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12610,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s8)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12609])).
% 1.78/1.77 tff(12611,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s8)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12610, 12608])).
% 1.78/1.77 tff(12612,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s8)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s8))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12613,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s8) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s8))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12612, 12611])).
% 1.78/1.77 tff(12614,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12613, 10853, 12607, 11532, 12606, 11533])).
% 1.78/1.77 tff(12615,plain,((~trans(s104, s8)) | until2p23(s8) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.77 tff(12616,plain,
% 1.78/1.77 (~trans(s104, s8)),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12615, 12216, 10843])).
% 1.78/1.77 tff(12617,assumption,(~until2p23(s71)), introduced(assumption)).
% 1.78/1.77 tff(12618,assumption,(trans(s104, s71)), introduced(assumption)).
% 1.78/1.77 tff(12619,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12620,plain,
% 1.78/1.77 (((~trans(s104, s71)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s71)) <=> (until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71)))),
% 1.78/1.77 inference(rewrite,[status(thm)],[])).
% 1.78/1.77 tff(12621,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s71)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71))))),
% 1.78/1.77 inference(monotonicity,[status(thm)],[12620])).
% 1.78/1.77 tff(12622,plain,
% 1.78/1.77 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s71)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71)))),
% 1.78/1.77 inference(transitivity,[status(thm)],[12621, 12619])).
% 1.78/1.77 tff(12623,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s71)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s71))),
% 1.78/1.77 inference(quant_inst,[status(thm)],[])).
% 1.78/1.77 tff(12624,plain,
% 1.78/1.77 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s71) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s71))),
% 1.78/1.77 inference(modus_ponens,[status(thm)],[12623, 12622])).
% 1.78/1.77 tff(12625,plain,
% 1.78/1.77 ($false),
% 1.78/1.77 inference(unit_resolution,[status(thm)],[12624, 10853, 12618, 11532, 12617, 11533])).
% 1.78/1.78 tff(12626,plain,((~trans(s104, s71)) | until2p23(s71) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.78 tff(12627,plain,
% 1.78/1.78 (~trans(s104, s71)),
% 1.78/1.78 inference(unit_resolution,[status(thm)],[12626, 11212, 10843])).
% 1.78/1.78 tff(12628,assumption,(~until2p23(s17)), introduced(assumption)).
% 1.78/1.78 tff(12629,assumption,(trans(s104, s17)), introduced(assumption)).
% 1.78/1.78 tff(12630,plain,
% 1.78/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17)))),
% 1.78/1.78 inference(rewrite,[status(thm)],[])).
% 1.78/1.78 tff(12631,plain,
% 1.78/1.78 (((~trans(s104, s17)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s17)) <=> (until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17)))),
% 1.78/1.78 inference(rewrite,[status(thm)],[])).
% 1.78/1.78 tff(12632,plain,
% 1.78/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s17)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17))))),
% 1.78/1.78 inference(monotonicity,[status(thm)],[12631])).
% 1.78/1.78 tff(12633,plain,
% 1.78/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s17)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17)))),
% 1.78/1.78 inference(transitivity,[status(thm)],[12632, 12630])).
% 1.78/1.78 tff(12634,plain,
% 1.78/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s17)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s17))),
% 1.78/1.78 inference(quant_inst,[status(thm)],[])).
% 1.85/1.78 tff(12635,plain,
% 1.85/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s17) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s17))),
% 1.85/1.78 inference(modus_ponens,[status(thm)],[12634, 12633])).
% 1.85/1.78 tff(12636,plain,
% 1.85/1.78 ($false),
% 1.85/1.78 inference(unit_resolution,[status(thm)],[12635, 10853, 12629, 11532, 12628, 11533])).
% 1.85/1.78 tff(12637,plain,((~trans(s104, s17)) | until2p23(s17) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.78 tff(12638,plain,
% 1.85/1.78 (~trans(s104, s17)),
% 1.85/1.78 inference(unit_resolution,[status(thm)],[12637, 11906, 10843])).
% 1.85/1.78 tff(12639,assumption,(~until2p23(s61)), introduced(assumption)).
% 1.85/1.78 tff(12640,assumption,(trans(s104, s61)), introduced(assumption)).
% 1.85/1.78 tff(12641,plain,
% 1.85/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61)))),
% 1.85/1.78 inference(rewrite,[status(thm)],[])).
% 1.85/1.78 tff(12642,plain,
% 1.85/1.78 (((~trans(s104, s61)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s61)) <=> (until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61)))),
% 1.85/1.78 inference(rewrite,[status(thm)],[])).
% 1.85/1.78 tff(12643,plain,
% 1.85/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s61)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61))))),
% 1.85/1.78 inference(monotonicity,[status(thm)],[12642])).
% 1.85/1.78 tff(12644,plain,
% 1.85/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s61)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61)))),
% 1.85/1.78 inference(transitivity,[status(thm)],[12643, 12641])).
% 1.85/1.78 tff(12645,plain,
% 1.85/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s61)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s61))),
% 1.85/1.78 inference(quant_inst,[status(thm)],[])).
% 1.85/1.78 tff(12646,plain,
% 1.85/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s61) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s61))),
% 1.85/1.78 inference(modus_ponens,[status(thm)],[12645, 12644])).
% 1.85/1.78 tff(12647,plain,
% 1.85/1.78 ($false),
% 1.85/1.78 inference(unit_resolution,[status(thm)],[12646, 10853, 12640, 11532, 12639, 11533])).
% 1.85/1.78 tff(12648,plain,((~trans(s104, s61)) | until2p23(s61) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.85/1.78 tff(12649,plain,
% 1.85/1.78 (~trans(s104, s61)),
% 1.85/1.78 inference(unit_resolution,[status(thm)],[12648, 11312, 10843])).
% 1.85/1.78 tff(12650,assumption,(~until2p23(s67)), introduced(assumption)).
% 1.85/1.78 tff(12651,assumption,(trans(s104, s67)), introduced(assumption)).
% 1.85/1.78 tff(12652,plain,
% 1.85/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67)))),
% 1.85/1.78 inference(rewrite,[status(thm)],[])).
% 1.85/1.78 tff(12653,plain,
% 1.85/1.78 (((~trans(s104, s67)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s67)) <=> (until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67)))),
% 1.85/1.78 inference(rewrite,[status(thm)],[])).
% 1.85/1.78 tff(12654,plain,
% 1.85/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s67)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67))))),
% 1.85/1.78 inference(monotonicity,[status(thm)],[12653])).
% 1.86/1.78 tff(12655,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s67)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12654, 12652])).
% 1.86/1.78 tff(12656,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s67)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s67))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12657,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s67) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s67))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12656, 12655])).
% 1.86/1.78 tff(12658,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12657, 10853, 12651, 11532, 12650, 11533])).
% 1.86/1.78 tff(12659,plain,((~trans(s104, s67)) | until2p23(s67) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12660,plain,
% 1.86/1.78 (~trans(s104, s67)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12659, 11252, 10843])).
% 1.86/1.78 tff(12661,assumption,(~until2p23(s65)), introduced(assumption)).
% 1.86/1.78 tff(12662,assumption,(trans(s104, s65)), introduced(assumption)).
% 1.86/1.78 tff(12663,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12664,plain,
% 1.86/1.78 (((~trans(s104, s65)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s65)) <=> (until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12665,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s65)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12664])).
% 1.86/1.78 tff(12666,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s65)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12665, 12663])).
% 1.86/1.78 tff(12667,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s65)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s65))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12668,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s65) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s65))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12667, 12666])).
% 1.86/1.78 tff(12669,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12668, 10853, 12662, 11532, 12661, 11533])).
% 1.86/1.78 tff(12670,plain,((~trans(s104, s65)) | until2p23(s65) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12671,plain,
% 1.86/1.78 (~trans(s104, s65)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12670, 11272, 10843])).
% 1.86/1.78 tff(12672,assumption,(~until2p23(s43)), introduced(assumption)).
% 1.86/1.78 tff(12673,assumption,(trans(s104, s43)), introduced(assumption)).
% 1.86/1.78 tff(12674,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12675,plain,
% 1.86/1.78 (((~trans(s104, s43)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s43)) <=> (until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12676,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s43)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12675])).
% 1.86/1.78 tff(12677,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s43)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12676, 12674])).
% 1.86/1.78 tff(12678,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s43)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s43))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12679,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s43) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s43))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12678, 12677])).
% 1.86/1.78 tff(12680,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12679, 10853, 12673, 11532, 12672, 11533])).
% 1.86/1.78 tff(12681,plain,((~trans(s104, s43)) | until2p23(s43) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12682,plain,
% 1.86/1.78 (~trans(s104, s43)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12681, 11492, 10843])).
% 1.86/1.78 tff(12683,assumption,(~until2p23(s83)), introduced(assumption)).
% 1.86/1.78 tff(12684,assumption,(trans(s104, s83)), introduced(assumption)).
% 1.86/1.78 tff(12685,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12686,plain,
% 1.86/1.78 (((~trans(s104, s83)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s83)) <=> (until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12687,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s83)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12686])).
% 1.86/1.78 tff(12688,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s83)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12687, 12685])).
% 1.86/1.78 tff(12689,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s83)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s83))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12690,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s83) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s83))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12689, 12688])).
% 1.86/1.78 tff(12691,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12690, 10853, 12684, 11532, 12683, 11533])).
% 1.86/1.78 tff(12692,plain,((~trans(s104, s83)) | until2p23(s83) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12693,plain,
% 1.86/1.78 (~trans(s104, s83)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12692, 11092, 10843])).
% 1.86/1.78 tff(12694,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s0, s1)) | until2p23(s1) | (~xuntil2p24(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s0, s1)) | until2p23(s1) | (~xuntil2p24(s0)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12695,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | ((~succ(s0, s1)) | until2p23(s1) | (~xuntil2p24(s0)))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12696,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p23(Y) | (~xuntil2p24(X)))) | (~succ(s0, s1)) | until2p23(s1) | (~xuntil2p24(s0))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12695, 12694])).
% 1.86/1.78 tff(12697,plain,
% 1.86/1.78 (until2p23(s1) | (~xuntil2p24(s0))),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12696, 42, 10882])).
% 1.86/1.78 tff(12698,plain,
% 1.86/1.78 (~xuntil2p24(s0)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12697, 12363])).
% 1.86/1.78 tff(12699,plain,
% 1.86/1.78 (((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s0) | xuntil2p24(s0) | (~until2p23(s0)))) <=> ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s0) | xuntil2p24(s0) | (~until2p23(s0)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12700,plain,
% 1.86/1.78 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | (node20(s0) | xuntil2p24(s0) | (~until2p23(s0)))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12701,plain,
% 1.86/1.78 ((~![X: $i] : (node20(X) | xuntil2p24(X) | (~until2p23(X)))) | node20(s0) | xuntil2p24(s0) | (~until2p23(s0))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12700, 12699])).
% 1.86/1.78 tff(12702,plain,
% 1.86/1.78 (xuntil2p24(s0) | (~until2p23(s0))),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12701, 10867, 9409])).
% 1.86/1.78 tff(12703,plain,
% 1.86/1.78 (~until2p23(s0)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12702, 12698])).
% 1.86/1.78 tff(12704,assumption,(~until2p23(s0)), introduced(assumption)).
% 1.86/1.78 tff(12705,assumption,(trans(s104, s0)), introduced(assumption)).
% 1.86/1.78 tff(12706,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12707,plain,
% 1.86/1.78 (((~trans(s104, s0)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0)) <=> ((~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12708,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s0)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12707])).
% 1.86/1.78 tff(12709,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s0)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12708, 12706])).
% 1.86/1.78 tff(12710,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s0)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12711,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s0) | (~trans(s104, s0))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12710, 12709])).
% 1.86/1.78 tff(12712,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12711, 10853, 12705, 11532, 11533, 12704])).
% 1.86/1.78 tff(12713,plain,((~trans(s104, s0)) | (~xuntil22(s104)) | until2p23(s0)), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12714,plain,
% 1.86/1.78 (~trans(s104, s0)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12713, 10843, 12703])).
% 1.86/1.78 tff(12715,assumption,(~until2p23(s50)), introduced(assumption)).
% 1.86/1.78 tff(12716,assumption,(trans(s104, s50)), introduced(assumption)).
% 1.86/1.78 tff(12717,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12718,plain,
% 1.86/1.78 (((~trans(s104, s50)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s50)) <=> (until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12719,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s50)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12718])).
% 1.86/1.78 tff(12720,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s50)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12719, 12717])).
% 1.86/1.78 tff(12721,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s50)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s50))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12722,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s50) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s50))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12721, 12720])).
% 1.86/1.78 tff(12723,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12722, 10853, 12716, 11532, 12715, 11533])).
% 1.86/1.78 tff(12724,plain,((~trans(s104, s50)) | until2p23(s50) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12725,plain,
% 1.86/1.78 (~trans(s104, s50)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12724, 11422, 10843])).
% 1.86/1.78 tff(12726,assumption,(~until2p23(s36)), introduced(assumption)).
% 1.86/1.78 tff(12727,assumption,(trans(s104, s36)), introduced(assumption)).
% 1.86/1.78 tff(12728,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12729,plain,
% 1.86/1.78 (((~trans(s104, s36)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s36)) <=> (until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12730,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s36)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12729])).
% 1.86/1.78 tff(12731,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s36)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12730, 12728])).
% 1.86/1.78 tff(12732,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s36)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s36))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12733,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s36) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s36))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12732, 12731])).
% 1.86/1.78 tff(12734,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12733, 10853, 12727, 11532, 12726, 11533])).
% 1.86/1.78 tff(12735,plain,((~trans(s104, s36)) | until2p23(s36) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12736,plain,
% 1.86/1.78 (~trans(s104, s36)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12735, 11584, 10843])).
% 1.86/1.78 tff(12737,assumption,(~until2p23(s41)), introduced(assumption)).
% 1.86/1.78 tff(12738,assumption,(trans(s104, s41)), introduced(assumption)).
% 1.86/1.78 tff(12739,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12740,plain,
% 1.86/1.78 (((~trans(s104, s41)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s41)) <=> (until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12741,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s41)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12740])).
% 1.86/1.78 tff(12742,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s41)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12741, 12739])).
% 1.86/1.78 tff(12743,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s41)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s41))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12744,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s41) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s41))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12743, 12742])).
% 1.86/1.78 tff(12745,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12744, 10853, 12738, 11532, 12737, 11533])).
% 1.86/1.78 tff(12746,plain,((~trans(s104, s41)) | until2p23(s41) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12747,plain,
% 1.86/1.78 (~trans(s104, s41)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12746, 11512, 10843])).
% 1.86/1.78 tff(12748,assumption,(~until2p23(s11)), introduced(assumption)).
% 1.86/1.78 tff(12749,assumption,(trans(s104, s11)), introduced(assumption)).
% 1.86/1.78 tff(12750,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12751,plain,
% 1.86/1.78 (((~trans(s104, s11)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s11)) <=> (until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12752,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s11)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12751])).
% 1.86/1.78 tff(12753,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s11)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12752, 12750])).
% 1.86/1.78 tff(12754,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s11)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s11))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12755,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s11) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s11))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12754, 12753])).
% 1.86/1.78 tff(12756,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12755, 10853, 12749, 11532, 12748, 11533])).
% 1.86/1.78 tff(12757,plain,((~trans(s104, s11)) | until2p23(s11) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12758,plain,
% 1.86/1.78 (~trans(s104, s11)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12757, 11966, 10843])).
% 1.86/1.78 tff(12759,assumption,(~until2p23(s89)), introduced(assumption)).
% 1.86/1.78 tff(12760,assumption,(trans(s104, s89)), introduced(assumption)).
% 1.86/1.78 tff(12761,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12762,plain,
% 1.86/1.78 (((~trans(s104, s89)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s89)) <=> (until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89)))),
% 1.86/1.78 inference(rewrite,[status(thm)],[])).
% 1.86/1.78 tff(12763,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s89)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89))))),
% 1.86/1.78 inference(monotonicity,[status(thm)],[12762])).
% 1.86/1.78 tff(12764,plain,
% 1.86/1.78 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s89)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89)))),
% 1.86/1.78 inference(transitivity,[status(thm)],[12763, 12761])).
% 1.86/1.78 tff(12765,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s89)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s89))),
% 1.86/1.78 inference(quant_inst,[status(thm)],[])).
% 1.86/1.78 tff(12766,plain,
% 1.86/1.78 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s89) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s89))),
% 1.86/1.78 inference(modus_ponens,[status(thm)],[12765, 12764])).
% 1.86/1.78 tff(12767,plain,
% 1.86/1.78 ($false),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12766, 10853, 12760, 11532, 12759, 11533])).
% 1.86/1.78 tff(12768,plain,((~trans(s104, s89)) | until2p23(s89) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.78 tff(12769,plain,
% 1.86/1.78 (~trans(s104, s89)),
% 1.86/1.78 inference(unit_resolution,[status(thm)],[12768, 11032, 10843])).
% 1.86/1.78 tff(12770,assumption,(~until2p23(s101)), introduced(assumption)).
% 1.86/1.78 tff(12771,assumption,(trans(s104, s101)), introduced(assumption)).
% 1.86/1.78 tff(12772,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12773,plain,
% 1.86/1.79 (((~trans(s104, s101)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s101)) <=> (until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12774,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s101)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12773])).
% 1.86/1.79 tff(12775,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s101)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12774, 12772])).
% 1.86/1.79 tff(12776,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s101)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s101))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12777,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s101) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s101))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12776, 12775])).
% 1.86/1.79 tff(12778,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12777, 10853, 12771, 11532, 12770, 11533])).
% 1.86/1.79 tff(12779,plain,((~trans(s104, s101)) | until2p23(s101) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12780,plain,
% 1.86/1.79 (~trans(s104, s101)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12779, 10912, 10843])).
% 1.86/1.79 tff(12781,assumption,(~until2p23(s45)), introduced(assumption)).
% 1.86/1.79 tff(12782,assumption,(trans(s104, s45)), introduced(assumption)).
% 1.86/1.79 tff(12783,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12784,plain,
% 1.86/1.79 (((~trans(s104, s45)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s45)) <=> (until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12785,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s45)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12784])).
% 1.86/1.79 tff(12786,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s45)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12785, 12783])).
% 1.86/1.79 tff(12787,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s45)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s45))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12788,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s45) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s45))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12787, 12786])).
% 1.86/1.79 tff(12789,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12788, 10853, 12782, 11532, 12781, 11533])).
% 1.86/1.79 tff(12790,plain,((~trans(s104, s45)) | until2p23(s45) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12791,plain,
% 1.86/1.79 (~trans(s104, s45)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12790, 11472, 10843])).
% 1.86/1.79 tff(12792,assumption,(~until2p23(s82)), introduced(assumption)).
% 1.86/1.79 tff(12793,assumption,(trans(s104, s82)), introduced(assumption)).
% 1.86/1.79 tff(12794,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12795,plain,
% 1.86/1.79 (((~trans(s104, s82)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s82)) <=> (until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12796,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s82)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12795])).
% 1.86/1.79 tff(12797,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s82)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12796, 12794])).
% 1.86/1.79 tff(12798,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s82)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s82))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12799,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s82) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s82))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12798, 12797])).
% 1.86/1.79 tff(12800,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12799, 10853, 12793, 11532, 12792, 11533])).
% 1.86/1.79 tff(12801,plain,((~trans(s104, s82)) | until2p23(s82) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12802,plain,
% 1.86/1.79 (~trans(s104, s82)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12801, 11102, 10843])).
% 1.86/1.79 tff(12803,assumption,(~until2p23(s98)), introduced(assumption)).
% 1.86/1.79 tff(12804,assumption,(trans(s104, s98)), introduced(assumption)).
% 1.86/1.79 tff(12805,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12806,plain,
% 1.86/1.79 (((~trans(s104, s98)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s98)) <=> (until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12807,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s98)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12806])).
% 1.86/1.79 tff(12808,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s98)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12807, 12805])).
% 1.86/1.79 tff(12809,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s98)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s98))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12810,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s98) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s98))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12809, 12808])).
% 1.86/1.79 tff(12811,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12810, 10853, 12804, 11532, 12803, 11533])).
% 1.86/1.79 tff(12812,plain,((~trans(s104, s98)) | until2p23(s98) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12813,plain,
% 1.86/1.79 (~trans(s104, s98)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12812, 10942, 10843])).
% 1.86/1.79 tff(12814,assumption,(~until2p23(s3)), introduced(assumption)).
% 1.86/1.79 tff(12815,assumption,(trans(s104, s3)), introduced(assumption)).
% 1.86/1.79 tff(12816,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12817,plain,
% 1.86/1.79 (((~trans(s104, s3)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s3)) <=> (until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12818,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s3)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12817])).
% 1.86/1.79 tff(12819,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s3)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12818, 12816])).
% 1.86/1.79 tff(12820,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s3)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s3))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12821,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s3) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s3))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12820, 12819])).
% 1.86/1.79 tff(12822,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12821, 10853, 12815, 11532, 12814, 11533])).
% 1.86/1.79 tff(12823,plain,((~trans(s104, s3)) | until2p23(s3) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12824,plain,
% 1.86/1.79 (~trans(s104, s3)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12823, 12266, 10843])).
% 1.86/1.79 tff(12825,assumption,(~until2p23(s18)), introduced(assumption)).
% 1.86/1.79 tff(12826,assumption,(trans(s104, s18)), introduced(assumption)).
% 1.86/1.79 tff(12827,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12828,plain,
% 1.86/1.79 (((~trans(s104, s18)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s18)) <=> (until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12829,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s18)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12828])).
% 1.86/1.79 tff(12830,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s18)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12829, 12827])).
% 1.86/1.79 tff(12831,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s18)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s18))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12832,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s18) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s18))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12831, 12830])).
% 1.86/1.79 tff(12833,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12832, 10853, 12826, 11532, 12825, 11533])).
% 1.86/1.79 tff(12834,plain,((~trans(s104, s18)) | until2p23(s18) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12835,plain,
% 1.86/1.79 (~trans(s104, s18)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12834, 11896, 10843])).
% 1.86/1.79 tff(12836,assumption,(~until2p23(s86)), introduced(assumption)).
% 1.86/1.79 tff(12837,assumption,(trans(s104, s86)), introduced(assumption)).
% 1.86/1.79 tff(12838,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12839,plain,
% 1.86/1.79 (((~trans(s104, s86)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s86)) <=> (until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12840,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s86)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12839])).
% 1.86/1.79 tff(12841,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s86)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12840, 12838])).
% 1.86/1.79 tff(12842,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s86)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s86))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12843,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s86) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s86))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12842, 12841])).
% 1.86/1.79 tff(12844,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12843, 10853, 12837, 11532, 12836, 11533])).
% 1.86/1.79 tff(12845,plain,((~trans(s104, s86)) | until2p23(s86) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12846,plain,
% 1.86/1.79 (~trans(s104, s86)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12845, 11062, 10843])).
% 1.86/1.79 tff(12847,assumption,(~until2p23(s92)), introduced(assumption)).
% 1.86/1.79 tff(12848,assumption,(trans(s104, s92)), introduced(assumption)).
% 1.86/1.79 tff(12849,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12850,plain,
% 1.86/1.79 (((~trans(s104, s92)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s92)) <=> (until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12851,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s92)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12850])).
% 1.86/1.79 tff(12852,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s92)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12851, 12849])).
% 1.86/1.79 tff(12853,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s92)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s92))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12854,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s92) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s92))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12853, 12852])).
% 1.86/1.79 tff(12855,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12854, 10853, 12848, 11532, 12847, 11533])).
% 1.86/1.79 tff(12856,plain,((~trans(s104, s92)) | until2p23(s92) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12857,plain,
% 1.86/1.79 (~trans(s104, s92)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12856, 11002, 10843])).
% 1.86/1.79 tff(12858,assumption,(~until2p23(s14)), introduced(assumption)).
% 1.86/1.79 tff(12859,assumption,(trans(s104, s14)), introduced(assumption)).
% 1.86/1.79 tff(12860,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12861,plain,
% 1.86/1.79 (((~trans(s104, s14)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s14)) <=> (until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12862,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s14)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12861])).
% 1.86/1.79 tff(12863,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s14)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12862, 12860])).
% 1.86/1.79 tff(12864,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s14)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s14))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12865,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s14) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s14))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12864, 12863])).
% 1.86/1.79 tff(12866,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12865, 10853, 12859, 11532, 12858, 11533])).
% 1.86/1.79 tff(12867,plain,((~trans(s104, s14)) | until2p23(s14) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12868,plain,
% 1.86/1.79 (~trans(s104, s14)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12867, 11936, 10843])).
% 1.86/1.79 tff(12869,assumption,(~until2p23(s77)), introduced(assumption)).
% 1.86/1.79 tff(12870,assumption,(trans(s104, s77)), introduced(assumption)).
% 1.86/1.79 tff(12871,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12872,plain,
% 1.86/1.79 (((~trans(s104, s77)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s77)) <=> (until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12873,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s77)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12872])).
% 1.86/1.79 tff(12874,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s77)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12873, 12871])).
% 1.86/1.79 tff(12875,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s77)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s77))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12876,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s77) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s77))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12875, 12874])).
% 1.86/1.79 tff(12877,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12876, 10853, 12870, 11532, 12869, 11533])).
% 1.86/1.79 tff(12878,plain,((~trans(s104, s77)) | until2p23(s77) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12879,plain,
% 1.86/1.79 (~trans(s104, s77)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12878, 11152, 10843])).
% 1.86/1.79 tff(12880,assumption,(~until2p23(s46)), introduced(assumption)).
% 1.86/1.79 tff(12881,assumption,(trans(s104, s46)), introduced(assumption)).
% 1.86/1.79 tff(12882,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12883,plain,
% 1.86/1.79 (((~trans(s104, s46)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s46)) <=> (until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12884,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s46)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12883])).
% 1.86/1.79 tff(12885,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s46)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12884, 12882])).
% 1.86/1.79 tff(12886,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s46)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s46))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12887,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s46) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s46))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12886, 12885])).
% 1.86/1.79 tff(12888,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12887, 10853, 12881, 11532, 12880, 11533])).
% 1.86/1.79 tff(12889,plain,((~trans(s104, s46)) | until2p23(s46) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12890,plain,
% 1.86/1.79 (~trans(s104, s46)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12889, 11462, 10843])).
% 1.86/1.79 tff(12891,assumption,(~until2p23(s84)), introduced(assumption)).
% 1.86/1.79 tff(12892,assumption,(trans(s104, s84)), introduced(assumption)).
% 1.86/1.79 tff(12893,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12894,plain,
% 1.86/1.79 (((~trans(s104, s84)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s84)) <=> (until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84)))),
% 1.86/1.79 inference(rewrite,[status(thm)],[])).
% 1.86/1.79 tff(12895,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s84)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84))))),
% 1.86/1.79 inference(monotonicity,[status(thm)],[12894])).
% 1.86/1.79 tff(12896,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s84)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84)))),
% 1.86/1.79 inference(transitivity,[status(thm)],[12895, 12893])).
% 1.86/1.79 tff(12897,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s84)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s84))),
% 1.86/1.79 inference(quant_inst,[status(thm)],[])).
% 1.86/1.79 tff(12898,plain,
% 1.86/1.79 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s84) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s84))),
% 1.86/1.79 inference(modus_ponens,[status(thm)],[12897, 12896])).
% 1.86/1.79 tff(12899,plain,
% 1.86/1.79 ($false),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12898, 10853, 12892, 11532, 12891, 11533])).
% 1.86/1.79 tff(12900,plain,((~trans(s104, s84)) | until2p23(s84) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.79 tff(12901,plain,
% 1.86/1.79 (~trans(s104, s84)),
% 1.86/1.79 inference(unit_resolution,[status(thm)],[12900, 11082, 10843])).
% 1.86/1.79 tff(12902,assumption,(~until2p23(s95)), introduced(assumption)).
% 1.86/1.79 tff(12903,assumption,(trans(s104, s95)), introduced(assumption)).
% 1.86/1.79 tff(12904,plain,
% 1.86/1.79 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12905,plain,
% 1.86/1.80 (((~trans(s104, s95)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s95)) <=> (until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12906,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s95)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12905])).
% 1.86/1.80 tff(12907,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s95)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12906, 12904])).
% 1.86/1.80 tff(12908,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s95)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s95))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12909,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s95) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s95))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12908, 12907])).
% 1.86/1.80 tff(12910,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12909, 10853, 12903, 11532, 12902, 11533])).
% 1.86/1.80 tff(12911,plain,((~trans(s104, s95)) | until2p23(s95) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12912,plain,
% 1.86/1.80 (~trans(s104, s95)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12911, 10972, 10843])).
% 1.86/1.80 tff(12913,assumption,(~until2p23(s87)), introduced(assumption)).
% 1.86/1.80 tff(12914,assumption,(trans(s104, s87)), introduced(assumption)).
% 1.86/1.80 tff(12915,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12916,plain,
% 1.86/1.80 (((~trans(s104, s87)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s87)) <=> (until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12917,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s87)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12916])).
% 1.86/1.80 tff(12918,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s87)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12917, 12915])).
% 1.86/1.80 tff(12919,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s87)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s87))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12920,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s87) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s87))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12919, 12918])).
% 1.86/1.80 tff(12921,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12920, 10853, 12914, 11532, 12913, 11533])).
% 1.86/1.80 tff(12922,plain,((~trans(s104, s87)) | until2p23(s87) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12923,plain,
% 1.86/1.80 (~trans(s104, s87)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12922, 11052, 10843])).
% 1.86/1.80 tff(12924,assumption,(~until2p23(s6)), introduced(assumption)).
% 1.86/1.80 tff(12925,assumption,(trans(s104, s6)), introduced(assumption)).
% 1.86/1.80 tff(12926,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12927,plain,
% 1.86/1.80 (((~trans(s104, s6)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s6)) <=> (until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12928,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s6)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12927])).
% 1.86/1.80 tff(12929,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s6)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12928, 12926])).
% 1.86/1.80 tff(12930,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s6)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s6))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12931,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s6) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s6))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12930, 12929])).
% 1.86/1.80 tff(12932,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12931, 10853, 12925, 11532, 12924, 11533])).
% 1.86/1.80 tff(12933,plain,((~trans(s104, s6)) | until2p23(s6) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12934,plain,
% 1.86/1.80 (~trans(s104, s6)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12933, 12236, 10843])).
% 1.86/1.80 tff(12935,assumption,(~until2p23(s47)), introduced(assumption)).
% 1.86/1.80 tff(12936,assumption,(trans(s104, s47)), introduced(assumption)).
% 1.86/1.80 tff(12937,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12938,plain,
% 1.86/1.80 (((~trans(s104, s47)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s47)) <=> (until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12939,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s47)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12938])).
% 1.86/1.80 tff(12940,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s47)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12939, 12937])).
% 1.86/1.80 tff(12941,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s47)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s47))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12942,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s47) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s47))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12941, 12940])).
% 1.86/1.80 tff(12943,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12942, 10853, 12936, 11532, 12935, 11533])).
% 1.86/1.80 tff(12944,plain,((~trans(s104, s47)) | until2p23(s47) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12945,plain,
% 1.86/1.80 (~trans(s104, s47)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12944, 11452, 10843])).
% 1.86/1.80 tff(12946,assumption,(~until2p23(s79)), introduced(assumption)).
% 1.86/1.80 tff(12947,assumption,(trans(s104, s79)), introduced(assumption)).
% 1.86/1.80 tff(12948,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12949,plain,
% 1.86/1.80 (((~trans(s104, s79)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s79)) <=> (until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12950,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s79)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12949])).
% 1.86/1.80 tff(12951,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s79)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12950, 12948])).
% 1.86/1.80 tff(12952,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s79)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s79))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12953,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s79) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s79))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12952, 12951])).
% 1.86/1.80 tff(12954,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12953, 10853, 12947, 11532, 12946, 11533])).
% 1.86/1.80 tff(12955,plain,((~trans(s104, s79)) | until2p23(s79) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12956,plain,
% 1.86/1.80 (~trans(s104, s79)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12955, 11132, 10843])).
% 1.86/1.80 tff(12957,assumption,(~until2p23(s30)), introduced(assumption)).
% 1.86/1.80 tff(12958,assumption,(trans(s104, s30)), introduced(assumption)).
% 1.86/1.80 tff(12959,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12960,plain,
% 1.86/1.80 (((~trans(s104, s30)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s30)) <=> (until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12961,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s30)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12960])).
% 1.86/1.80 tff(12962,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s30)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12961, 12959])).
% 1.86/1.80 tff(12963,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s30)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s30))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12964,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s30) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s30))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12963, 12962])).
% 1.86/1.80 tff(12965,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12964, 10853, 12958, 11532, 12957, 11533])).
% 1.86/1.80 tff(12966,plain,((~trans(s104, s30)) | until2p23(s30) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12967,plain,
% 1.86/1.80 (~trans(s104, s30)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12966, 11655, 10843])).
% 1.86/1.80 tff(12968,assumption,(~until2p23(s44)), introduced(assumption)).
% 1.86/1.80 tff(12969,assumption,(trans(s104, s44)), introduced(assumption)).
% 1.86/1.80 tff(12970,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12971,plain,
% 1.86/1.80 (((~trans(s104, s44)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s44)) <=> (until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12972,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s44)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12971])).
% 1.86/1.80 tff(12973,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s44)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12972, 12970])).
% 1.86/1.80 tff(12974,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s44)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s44))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12975,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s44) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s44))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12974, 12973])).
% 1.86/1.80 tff(12976,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12975, 10853, 12969, 11532, 12968, 11533])).
% 1.86/1.80 tff(12977,plain,((~trans(s104, s44)) | until2p23(s44) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12978,plain,
% 1.86/1.80 (~trans(s104, s44)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12977, 11482, 10843])).
% 1.86/1.80 tff(12979,assumption,(~until2p23(s94)), introduced(assumption)).
% 1.86/1.80 tff(12980,assumption,(trans(s104, s94)), introduced(assumption)).
% 1.86/1.80 tff(12981,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12982,plain,
% 1.86/1.80 (((~trans(s104, s94)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s94)) <=> (until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12983,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s94)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12982])).
% 1.86/1.80 tff(12984,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s94)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12983, 12981])).
% 1.86/1.80 tff(12985,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s94)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s94))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12986,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s94) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s94))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12985, 12984])).
% 1.86/1.80 tff(12987,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12986, 10853, 12980, 11532, 12979, 11533])).
% 1.86/1.80 tff(12988,plain,((~trans(s104, s94)) | until2p23(s94) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(12989,plain,
% 1.86/1.80 (~trans(s104, s94)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12988, 10982, 10843])).
% 1.86/1.80 tff(12990,assumption,(~until2p23(s90)), introduced(assumption)).
% 1.86/1.80 tff(12991,assumption,(trans(s104, s90)), introduced(assumption)).
% 1.86/1.80 tff(12992,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12993,plain,
% 1.86/1.80 (((~trans(s104, s90)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s90)) <=> (until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(12994,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s90)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[12993])).
% 1.86/1.80 tff(12995,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s90)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[12994, 12992])).
% 1.86/1.80 tff(12996,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s90)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s90))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(12997,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s90) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s90))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[12996, 12995])).
% 1.86/1.80 tff(12998,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12997, 10853, 12991, 11532, 12990, 11533])).
% 1.86/1.80 tff(12999,plain,((~trans(s104, s90)) | until2p23(s90) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(13000,plain,
% 1.86/1.80 (~trans(s104, s90)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[12999, 11022, 10843])).
% 1.86/1.80 tff(13001,assumption,(~until2p23(s42)), introduced(assumption)).
% 1.86/1.80 tff(13002,assumption,(trans(s104, s42)), introduced(assumption)).
% 1.86/1.80 tff(13003,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13004,plain,
% 1.86/1.80 (((~trans(s104, s42)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s42)) <=> (until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13005,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s42)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[13004])).
% 1.86/1.80 tff(13006,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s42)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[13005, 13003])).
% 1.86/1.80 tff(13007,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s42)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s42))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(13008,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s42) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s42))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[13007, 13006])).
% 1.86/1.80 tff(13009,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13008, 10853, 13002, 11532, 13001, 11533])).
% 1.86/1.80 tff(13010,plain,((~trans(s104, s42)) | until2p23(s42) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(13011,plain,
% 1.86/1.80 (~trans(s104, s42)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13010, 11502, 10843])).
% 1.86/1.80 tff(13012,assumption,(~until2p23(s34)), introduced(assumption)).
% 1.86/1.80 tff(13013,assumption,(trans(s104, s34)), introduced(assumption)).
% 1.86/1.80 tff(13014,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13015,plain,
% 1.86/1.80 (((~trans(s104, s34)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s34)) <=> (until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13016,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s34)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[13015])).
% 1.86/1.80 tff(13017,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s34)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[13016, 13014])).
% 1.86/1.80 tff(13018,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s34)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s34))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(13019,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s34) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s34))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[13018, 13017])).
% 1.86/1.80 tff(13020,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13019, 10853, 13013, 11532, 13012, 11533])).
% 1.86/1.80 tff(13021,plain,((~trans(s104, s34)) | until2p23(s34) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(13022,plain,
% 1.86/1.80 (~trans(s104, s34)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13021, 11604, 10843])).
% 1.86/1.80 tff(13023,assumption,(~until2p23(s100)), introduced(assumption)).
% 1.86/1.80 tff(13024,assumption,(trans(s104, s100)), introduced(assumption)).
% 1.86/1.80 tff(13025,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13026,plain,
% 1.86/1.80 (((~trans(s104, s100)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s100)) <=> (until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13027,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s100)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100))))),
% 1.86/1.80 inference(monotonicity,[status(thm)],[13026])).
% 1.86/1.80 tff(13028,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s100)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100)))),
% 1.86/1.80 inference(transitivity,[status(thm)],[13027, 13025])).
% 1.86/1.80 tff(13029,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s100)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s100))),
% 1.86/1.80 inference(quant_inst,[status(thm)],[])).
% 1.86/1.80 tff(13030,plain,
% 1.86/1.80 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s100) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s100))),
% 1.86/1.80 inference(modus_ponens,[status(thm)],[13029, 13028])).
% 1.86/1.80 tff(13031,plain,
% 1.86/1.80 ($false),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13030, 10853, 13024, 11532, 13023, 11533])).
% 1.86/1.80 tff(13032,plain,((~trans(s104, s100)) | until2p23(s100) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.80 tff(13033,plain,
% 1.86/1.80 (~trans(s104, s100)),
% 1.86/1.80 inference(unit_resolution,[status(thm)],[13032, 10922, 10843])).
% 1.86/1.80 tff(13034,assumption,(~until2p23(s26)), introduced(assumption)).
% 1.86/1.80 tff(13035,assumption,(trans(s104, s26)), introduced(assumption)).
% 1.86/1.80 tff(13036,plain,
% 1.86/1.80 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26)))),
% 1.86/1.80 inference(rewrite,[status(thm)],[])).
% 1.86/1.80 tff(13037,plain,
% 1.86/1.81 (((~trans(s104, s26)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s26)) <=> (until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13038,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s26)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26))))),
% 1.86/1.81 inference(monotonicity,[status(thm)],[13037])).
% 1.86/1.81 tff(13039,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s26)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26)))),
% 1.86/1.81 inference(transitivity,[status(thm)],[13038, 13036])).
% 1.86/1.81 tff(13040,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s26)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s26))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13041,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s26) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s26))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13040, 13039])).
% 1.86/1.81 tff(13042,plain,
% 1.86/1.81 ($false),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13041, 10853, 13035, 11532, 13034, 11533])).
% 1.86/1.81 tff(13043,plain,((~trans(s104, s26)) | until2p23(s26) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.81 tff(13044,plain,
% 1.86/1.81 (~trans(s104, s26)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13043, 11695, 10843])).
% 1.86/1.81 tff(13045,assumption,(~until2p23(s85)), introduced(assumption)).
% 1.86/1.81 tff(13046,assumption,(trans(s104, s85)), introduced(assumption)).
% 1.86/1.81 tff(13047,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13048,plain,
% 1.86/1.81 (((~trans(s104, s85)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s85)) <=> (until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13049,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s85)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85))))),
% 1.86/1.81 inference(monotonicity,[status(thm)],[13048])).
% 1.86/1.81 tff(13050,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s85)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85)))),
% 1.86/1.81 inference(transitivity,[status(thm)],[13049, 13047])).
% 1.86/1.81 tff(13051,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s85)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s85))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13052,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s85) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s85))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13051, 13050])).
% 1.86/1.81 tff(13053,plain,
% 1.86/1.81 ($false),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13052, 10853, 13046, 11532, 13045, 11533])).
% 1.86/1.81 tff(13054,plain,((~trans(s104, s85)) | until2p23(s85) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.86/1.81 tff(13055,plain,
% 1.86/1.81 (~trans(s104, s85)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13054, 11072, 10843])).
% 1.86/1.81 tff(13056,assumption,(node14(s104, s104)), introduced(assumption)).
% 1.86/1.81 tff(13057,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s101, c_t2) | (~node15(s101)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s101, c_t2) | (~node15(s101)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13058,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | (m_main_v_state2(s101, c_t2) | (~node15(s101)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13059,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node15(X)))) | m_main_v_state2(s101, c_t2) | (~node15(s101))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13058, 13057])).
% 1.86/1.81 tff(13060,plain,
% 1.86/1.81 (~node15(s101)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13059, 103, 8448])).
% 1.86/1.81 tff(13061,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s101, s102)) | node18(s101, s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s101, s102)) | node18(s101, s102))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13062,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | ((~trans(s101, s102)) | node18(s101, s102))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13063,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node18(X, Y))) | (~trans(s101, s102)) | node18(s101, s102)),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13062, 13061])).
% 1.86/1.81 tff(13064,plain,
% 1.86/1.81 (node18(s101, s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13063, 125, 8459])).
% 1.86/1.81 tff(13065,plain,
% 1.86/1.81 (((~![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(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, 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(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13066,plain,
% 1.86/1.81 (((~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node15(s101) | (~node18(s101, s102)) | m_main_v_turn(s102, c_1)) <=> (node15(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13067,plain,
% 1.86/1.81 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node15(s101) | (~node18(s101, s102)) | m_main_v_turn(s102, 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(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1)))),
% 1.86/1.81 inference(monotonicity,[status(thm)],[13066])).
% 1.86/1.81 tff(13068,plain,
% 1.86/1.81 (((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node15(s101) | (~node18(s101, s102)) | m_main_v_turn(s102, 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(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1))),
% 1.86/1.81 inference(transitivity,[status(thm)],[13067, 13065])).
% 1.86/1.81 tff(13069,plain,
% 1.86/1.81 ((~![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(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | node15(s101) | (~node18(s101, s102)) | m_main_v_turn(s102, c_1))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13070,plain,
% 1.86/1.81 ((~![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(s101) | (~node18(s101, s102)) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1)),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13069, 13068])).
% 1.86/1.81 tff(13071,plain,
% 1.86/1.81 (node15(s101) | (~m_main_v_state1(s101, c_t1)) | (~m_main_v_state2(s101, c_n2)) | m_main_v_turn(s102, c_1)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13070, 992, 13064])).
% 1.86/1.81 tff(13072,plain,
% 1.86/1.81 (m_main_v_turn(s102, c_1)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13071, 13060, 8376, 8444])).
% 1.86/1.81 tff(13073,plain,
% 1.86/1.81 (((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s102, c_1)) | (~m_main_v_turn(s102, c_2)))) <=> ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s102, c_1)) | (~m_main_v_turn(s102, c_2)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13074,plain,
% 1.86/1.81 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | ((~m_main_v_turn(s102, c_1)) | (~m_main_v_turn(s102, c_2)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13075,plain,
% 1.86/1.81 ((~![X: $i] : ((~m_main_v_turn(X, c_1)) | (~m_main_v_turn(X, c_2)))) | (~m_main_v_turn(s102, c_1)) | (~m_main_v_turn(s102, c_2))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13074, 13073])).
% 1.86/1.81 tff(13076,plain,
% 1.86/1.81 (~m_main_v_turn(s102, c_2)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13075, 156, 13072])).
% 1.86/1.81 tff(13077,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s102, c_2) | (~node12(s102)))) <=> ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s102, c_2) | (~node12(s102)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13078,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | (m_main_v_turn(s102, c_2) | (~node12(s102)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13079,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_turn(X, c_2) | (~node12(X)))) | m_main_v_turn(s102, c_2) | (~node12(s102))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13078, 13077])).
% 1.86/1.81 tff(13080,plain,
% 1.86/1.81 (~node12(s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13079, 184, 13076])).
% 1.86/1.81 tff(13081,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s102, c_n2) | (~node8(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s102, c_n2) | (~node8(s102)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13082,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s102, c_n2) | (~node8(s102)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13083,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s102, c_n2) | (~node8(s102))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13082, 13081])).
% 1.86/1.81 tff(13084,plain,
% 1.86/1.81 (~node8(s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13083, 271, 8492])).
% 1.86/1.81 tff(13085,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s102, c_n2) | (~node9(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s102, c_n2) | (~node9(s102)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13086,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s102, c_n2) | (~node9(s102)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13087,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s102, c_n2) | (~node9(s102))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13086, 13085])).
% 1.86/1.81 tff(13088,plain,
% 1.86/1.81 (~node9(s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13087, 88, 8492])).
% 1.86/1.81 tff(13089,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s102, c_n2) | (~node10(s102)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s102, c_n2) | (~node10(s102)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13090,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s102, c_n2) | (~node10(s102)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13091,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s102, c_n2) | (~node10(s102))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13090, 13089])).
% 1.86/1.81 tff(13092,plain,
% 1.86/1.81 (~node10(s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13091, 249, 8492])).
% 1.86/1.81 tff(13093,plain,
% 1.86/1.81 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s102, c_n1) | (~node11(s102)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s102, c_n1) | (~node11(s102)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13094,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s102, c_n1) | (~node11(s102)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13095,plain,
% 1.86/1.81 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s102, c_n1) | (~node11(s102))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13094, 13093])).
% 1.86/1.81 tff(13096,plain,
% 1.86/1.81 (~node11(s102)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13095, 238, 8512])).
% 1.86/1.81 tff(13097,plain,
% 1.86/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s102, s103)) | node14(s102, s103))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s102, s103)) | node14(s102, s103))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13098,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s102, s103)) | node14(s102, s103))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13099,plain,
% 1.86/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s102, s103)) | node14(s102, s103)),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13098, 13097])).
% 1.86/1.81 tff(13100,plain,
% 1.86/1.81 (node14(s102, s103)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13099, 7, 8523])).
% 1.86/1.81 tff(13101,plain,
% 1.86/1.81 (((~![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(s102, c_c2) | node9(s102) | node8(s102) | node10(s102) | node11(s102) | node12(s102) | node13(s102, s103) | (~node14(s102, s103)))) <=> ((~![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(s102, c_c2) | node9(s102) | node8(s102) | node10(s102) | node11(s102) | node12(s102) | node13(s102, s103) | (~node14(s102, s103)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.86/1.81 tff(13102,plain,
% 1.86/1.81 ((~![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(s102, c_c2) | node9(s102) | node8(s102) | node10(s102) | node11(s102) | node12(s102) | node13(s102, s103) | (~node14(s102, s103)))),
% 1.86/1.81 inference(quant_inst,[status(thm)],[])).
% 1.86/1.81 tff(13103,plain,
% 1.86/1.81 ((~![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(s102, c_c2) | node9(s102) | node8(s102) | node10(s102) | node11(s102) | node12(s102) | node13(s102, s103) | (~node14(s102, s103))),
% 1.86/1.81 inference(modus_ponens,[status(thm)],[13102, 13101])).
% 1.86/1.81 tff(13104,plain,
% 1.86/1.81 (m_main_v_state2(s102, c_c2) | node9(s102) | node8(s102) | node10(s102) | node11(s102) | node12(s102) | node13(s102, s103)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13103, 296, 13100])).
% 1.86/1.81 tff(13105,plain,
% 1.86/1.81 (node13(s102, s103)),
% 1.86/1.81 inference(unit_resolution,[status(thm)],[13104, 13096, 8500, 13092, 13088, 13084, 13080])).
% 1.86/1.81 tff(13106,plain,
% 1.86/1.81 (((~![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(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103)))) <=> ((~![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(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103)))),
% 1.86/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13107,plain,
% 1.90/1.81 (((~node13(s102, s103)) | m_main_v_state2(s102, c_n2) | (~m_main_v_state2(s103, c_n2))) <=> (m_main_v_state2(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13108,plain,
% 1.90/1.81 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s102, s103)) | m_main_v_state2(s102, c_n2) | (~m_main_v_state2(s103, 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(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103))))),
% 1.90/1.81 inference(monotonicity,[status(thm)],[13107])).
% 1.90/1.81 tff(13109,plain,
% 1.90/1.81 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s102, s103)) | m_main_v_state2(s102, c_n2) | (~m_main_v_state2(s103, 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(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103)))),
% 1.90/1.81 inference(transitivity,[status(thm)],[13108, 13106])).
% 1.90/1.81 tff(13110,plain,
% 1.90/1.81 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | m_main_v_state2(X, V) | (~m_main_v_state2(Y, V)))) | ((~node13(s102, s103)) | m_main_v_state2(s102, c_n2) | (~m_main_v_state2(s103, c_n2)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13111,plain,
% 1.90/1.81 ((~![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(s102, c_n2) | (~m_main_v_state2(s103, c_n2)) | (~node13(s102, s103))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13110, 13109])).
% 1.90/1.81 tff(13112,plain,
% 1.90/1.81 (~m_main_v_state2(s103, c_n2)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13111, 311, 8492, 13105])).
% 1.90/1.81 tff(13113,plain,
% 1.90/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s103, c_n2) | (~node9(s103)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s103, c_n2) | (~node9(s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13114,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | (m_main_v_state2(s103, c_n2) | (~node9(s103)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13115,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node9(X)))) | m_main_v_state2(s103, c_n2) | (~node9(s103))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13114, 13113])).
% 1.90/1.81 tff(13116,plain,
% 1.90/1.81 (~node9(s103)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13115, 88, 13112])).
% 1.90/1.81 tff(13117,plain,
% 1.90/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s103, c_n2) | (~node10(s103)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s103, c_n2) | (~node10(s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13118,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | (m_main_v_state2(s103, c_n2) | (~node10(s103)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13119,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node10(X)))) | m_main_v_state2(s103, c_n2) | (~node10(s103))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13118, 13117])).
% 1.90/1.81 tff(13120,plain,
% 1.90/1.81 (~node10(s103)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13119, 249, 13112])).
% 1.90/1.81 tff(13121,plain,
% 1.90/1.81 (((~![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(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103)))) <=> ((~![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(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13122,plain,
% 1.90/1.81 (((~node13(s102, s103)) | (~m_main_v_state2(s102, c_t2)) | m_main_v_state2(s103, c_t2)) <=> ((~m_main_v_state2(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13123,plain,
% 1.90/1.81 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s102, s103)) | (~m_main_v_state2(s102, c_t2)) | m_main_v_state2(s103, 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(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103))))),
% 1.90/1.81 inference(monotonicity,[status(thm)],[13122])).
% 1.90/1.81 tff(13124,plain,
% 1.90/1.81 (((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s102, s103)) | (~m_main_v_state2(s102, c_t2)) | m_main_v_state2(s103, 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(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103)))),
% 1.90/1.81 inference(transitivity,[status(thm)],[13123, 13121])).
% 1.90/1.81 tff(13125,plain,
% 1.90/1.81 ((~![V: $i, Y: $i, X: $i] : ((~node13(X, Y)) | (~m_main_v_state2(X, V)) | m_main_v_state2(Y, V))) | ((~node13(s102, s103)) | (~m_main_v_state2(s102, c_t2)) | m_main_v_state2(s103, c_t2))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13126,plain,
% 1.90/1.81 ((~![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(s102, c_t2)) | m_main_v_state2(s103, c_t2) | (~node13(s102, s103))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13125, 13124])).
% 1.90/1.81 tff(13127,plain,
% 1.90/1.81 (m_main_v_state2(s103, c_t2)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13126, 518, 8488, 13105])).
% 1.90/1.81 tff(13128,plain,
% 1.90/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s103, c_n2) | (~node8(s103)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s103, c_n2) | (~node8(s103)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13129,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s103, c_n2) | (~node8(s103)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13130,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s103, c_n2) | (~node8(s103))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13129, 13128])).
% 1.90/1.81 tff(13131,plain,
% 1.90/1.81 (~node8(s103)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13130, 271, 13112])).
% 1.90/1.81 tff(13132,plain,
% 1.90/1.81 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s103, s104)) | trans(s103, s104))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s103, s104)) | trans(s103, s104))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13133,plain,
% 1.90/1.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s103, s104)) | trans(s103, s104))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13134,plain,
% 1.90/1.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s103, s104)) | trans(s103, s104)),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13133, 13132])).
% 1.90/1.81 tff(13135,plain,
% 1.90/1.81 (trans(s103, s104)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13134, 10830, 39])).
% 1.90/1.81 tff(13136,plain,
% 1.90/1.81 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s103, s104)) | node14(s103, s104))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s103, s104)) | node14(s103, s104))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13137,plain,
% 1.90/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s103, s104)) | node14(s103, s104))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13138,plain,
% 1.90/1.81 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s103, s104)) | node14(s103, s104)),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13137, 13136])).
% 1.90/1.81 tff(13139,plain,
% 1.90/1.81 (node14(s103, s104)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13138, 7, 13135])).
% 1.90/1.81 tff(13140,plain,
% 1.90/1.81 (((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | node9(s103) | node8(s103) | node10(s103) | (~node14(s103, s104)) | m_main_v_state2(s104, 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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | node9(s103) | node8(s103) | node10(s103) | (~node14(s103, s104)) | m_main_v_state2(s104, c_c2))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13141,plain,
% 1.90/1.81 ((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | node9(s103) | node8(s103) | node10(s103) | (~node14(s103, s104)) | m_main_v_state2(s104, c_c2))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13142,plain,
% 1.90/1.81 ((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | node9(s103) | node8(s103) | node10(s103) | (~node14(s103, s104)) | m_main_v_state2(s104, c_c2)),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13141, 13140])).
% 1.90/1.81 tff(13143,plain,
% 1.90/1.81 ((~m_main_v_state1(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | node9(s103) | node8(s103) | node10(s103) | m_main_v_state2(s104, c_c2)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13142, 617, 13139])).
% 1.90/1.81 tff(13144,plain,
% 1.90/1.81 (m_main_v_state2(s104, c_c2)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13143, 13131, 8535, 13127, 13120, 13116])).
% 1.90/1.81 tff(13145,plain,
% 1.90/1.81 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13146,plain,
% 1.90/1.81 (((~m_main_v_state2(s104, c_n2)) | (~m_main_v_state2(s104, c_c2))) <=> ((~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13147,plain,
% 1.90/1.81 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_n2)) | (~m_main_v_state2(s104, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2))))),
% 1.90/1.81 inference(monotonicity,[status(thm)],[13146])).
% 1.90/1.81 tff(13148,plain,
% 1.90/1.81 (((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_n2)) | (~m_main_v_state2(s104, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2)))),
% 1.90/1.81 inference(transitivity,[status(thm)],[13147, 13145])).
% 1.90/1.81 tff(13149,plain,
% 1.90/1.81 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_n2)) | (~m_main_v_state2(s104, c_c2)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13150,plain,
% 1.90/1.81 ((~![X: $i] : ((~m_main_v_state2(X, c_n2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s104, c_c2)) | (~m_main_v_state2(s104, c_n2))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13149, 13148])).
% 1.90/1.81 tff(13151,plain,
% 1.90/1.81 (~m_main_v_state2(s104, c_n2)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13150, 697, 13144])).
% 1.90/1.81 tff(13152,plain,
% 1.90/1.81 (((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s104, c_n2) | (~node8(s104)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s104, c_n2) | (~node8(s104)))),
% 1.90/1.81 inference(rewrite,[status(thm)],[])).
% 1.90/1.81 tff(13153,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | (m_main_v_state2(s104, c_n2) | (~node8(s104)))),
% 1.90/1.81 inference(quant_inst,[status(thm)],[])).
% 1.90/1.81 tff(13154,plain,
% 1.90/1.81 ((~![X: $i] : (m_main_v_state2(X, c_n2) | (~node8(X)))) | m_main_v_state2(s104, c_n2) | (~node8(s104))),
% 1.90/1.81 inference(modus_ponens,[status(thm)],[13153, 13152])).
% 1.90/1.81 tff(13155,plain,
% 1.90/1.81 (~node8(s104)),
% 1.90/1.81 inference(unit_resolution,[status(thm)],[13154, 271, 13151])).
% 1.90/1.81 tff(13156,plain,
% 1.90/1.81 (((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_t2)) | (~m_main_v_state2(s104, c_c2)))) <=> ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s104, c_t2)) | (~m_main_v_state2(s104, c_c2)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13157,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | ((~m_main_v_state2(s104, c_t2)) | (~m_main_v_state2(s104, c_c2)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13158,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state2(X, c_t2)) | (~m_main_v_state2(X, c_c2)))) | (~m_main_v_state2(s104, c_t2)) | (~m_main_v_state2(s104, c_c2))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13157, 13156])).
% 1.90/1.82 tff(13159,plain,
% 1.90/1.82 (~m_main_v_state2(s104, c_t2)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13158, 260, 13144])).
% 1.90/1.82 tff(13160,plain,
% 1.90/1.82 (((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s104, c_t2) | (~node12(s104)))) <=> ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s104, c_t2) | (~node12(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13161,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | (m_main_v_state2(s104, c_t2) | (~node12(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13162,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state2(X, c_t2) | (~node12(X)))) | m_main_v_state2(s104, c_t2) | (~node12(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13161, 13160])).
% 1.90/1.82 tff(13163,plain,
% 1.90/1.82 (~node12(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13162, 633, 13159])).
% 1.90/1.82 tff(13164,plain,
% 1.90/1.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s103, s104)) | node7(s103, s104))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s103, s104)) | node7(s103, s104))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13165,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | ((~trans(s103, s104)) | node7(s103, s104))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13166,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node7(X, Y))) | (~trans(s103, s104)) | node7(s103, s104)),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13165, 13164])).
% 1.90/1.82 tff(13167,plain,
% 1.90/1.82 (node7(s103, s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13166, 206, 13135])).
% 1.90/1.82 tff(13168,plain,
% 1.90/1.82 (((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | (~node7(s103, s104)) | m_main_v_state1(s104, 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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | (~node7(s103, s104)) | m_main_v_state1(s104, c_t1))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13169,plain,
% 1.90/1.82 ((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | (~node7(s103, s104)) | m_main_v_state1(s104, c_t1))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13170,plain,
% 1.90/1.82 ((~![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(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | (~node7(s103, s104)) | m_main_v_state1(s104, c_t1)),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13169, 13168])).
% 1.90/1.82 tff(13171,plain,
% 1.90/1.82 ((~m_main_v_state1(s103, c_n1)) | (~m_main_v_state2(s103, c_t2)) | m_main_v_state1(s104, c_t1)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13170, 651, 13167])).
% 1.90/1.82 tff(13172,plain,
% 1.90/1.82 (m_main_v_state1(s104, c_t1)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13171, 13127, 8535])).
% 1.90/1.82 tff(13173,plain,
% 1.90/1.82 (((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s104, c_n1)) | (~m_main_v_state1(s104, c_t1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s104, c_n1)) | (~m_main_v_state1(s104, c_t1)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13174,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | ((~m_main_v_state1(s104, c_n1)) | (~m_main_v_state1(s104, c_t1)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13175,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state1(X, c_n1)) | (~m_main_v_state1(X, c_t1)))) | (~m_main_v_state1(s104, c_n1)) | (~m_main_v_state1(s104, c_t1))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13174, 13173])).
% 1.90/1.82 tff(13176,plain,
% 1.90/1.82 (~m_main_v_state1(s104, c_n1)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13175, 17, 13172])).
% 1.90/1.82 tff(13177,plain,
% 1.90/1.82 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s104, c_n1) | (~node9(s104)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s104, c_n1) | (~node9(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13178,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | (m_main_v_state1(s104, c_n1) | (~node9(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13179,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node9(X)))) | m_main_v_state1(s104, c_n1) | (~node9(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13178, 13177])).
% 1.90/1.82 tff(13180,plain,
% 1.90/1.82 (~node9(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13179, 686, 13176])).
% 1.90/1.82 tff(13181,plain,
% 1.90/1.82 (((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s104, c_n1) | (~node11(s104)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s104, c_n1) | (~node11(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13182,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | (m_main_v_state1(s104, c_n1) | (~node11(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13183,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_n1) | (~node11(X)))) | m_main_v_state1(s104, c_n1) | (~node11(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13182, 13181])).
% 1.90/1.82 tff(13184,plain,
% 1.90/1.82 (~node11(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13183, 238, 13176])).
% 1.90/1.82 tff(13185,plain,
% 1.90/1.82 (((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s104, c_t1)) | (~m_main_v_state1(s104, c_c1)))) <=> ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s104, c_t1)) | (~m_main_v_state1(s104, c_c1)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13186,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | ((~m_main_v_state1(s104, c_t1)) | (~m_main_v_state1(s104, c_c1)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13187,plain,
% 1.90/1.82 ((~![X: $i] : ((~m_main_v_state1(X, c_t1)) | (~m_main_v_state1(X, c_c1)))) | (~m_main_v_state1(s104, c_t1)) | (~m_main_v_state1(s104, c_c1))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13186, 13185])).
% 1.90/1.82 tff(13188,plain,
% 1.90/1.82 (~m_main_v_state1(s104, c_c1)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13187, 539, 13172])).
% 1.90/1.82 tff(13189,plain,
% 1.90/1.82 (((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s104, c_c1) | (~node10(s104)))) <=> ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s104, c_c1) | (~node10(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13190,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | (m_main_v_state1(s104, c_c1) | (~node10(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13191,plain,
% 1.90/1.82 ((~![X: $i] : (m_main_v_state1(X, c_c1) | (~node10(X)))) | m_main_v_state1(s104, c_c1) | (~node10(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13190, 13189])).
% 1.90/1.82 tff(13192,plain,
% 1.90/1.82 (~node10(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13191, 675, 13188])).
% 1.90/1.82 tff(13193,plain,
% 1.90/1.82 (((~![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(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104)))) <=> ((~![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(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13194,plain,
% 1.90/1.82 (((~m_main_v_state2(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s104)) | m_main_v_state2(s104, c_n2)) <=> (m_main_v_state2(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13195,plain,
% 1.90/1.82 (((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s104)) | m_main_v_state2(s104, 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(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104))))),
% 1.90/1.82 inference(monotonicity,[status(thm)],[13194])).
% 1.90/1.82 tff(13196,plain,
% 1.90/1.82 (((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s104)) | m_main_v_state2(s104, 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(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104)))),
% 1.90/1.82 inference(transitivity,[status(thm)],[13195, 13193])).
% 1.90/1.82 tff(13197,plain,
% 1.90/1.82 ((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s104)) | m_main_v_state2(s104, c_n2))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13198,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s104, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13197, 13196])).
% 1.90/1.82 tff(13199,plain,
% 1.90/1.82 ($false),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13198, 726, 13151, 13144, 13192, 13184, 13180, 13163, 13155, 13056])).
% 1.90/1.82 tff(13200,plain,(~node14(s104, s104)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.82 tff(13201,plain,
% 1.90/1.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s104, s104)) | node14(s104, s104))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s104, s104)) | node14(s104, s104))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13202,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s104, s104)) | node14(s104, s104))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13203,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s104, s104)) | node14(s104, s104)),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13202, 13201])).
% 1.90/1.82 tff(13204,plain,
% 1.90/1.82 (~trans(s104, s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13203, 7, 13200])).
% 1.90/1.82 tff(13205,assumption,(~loop), introduced(assumption)).
% 1.90/1.82 tff(13206,plain,
% 1.90/1.82 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil22(X))) <=> (loop | (~last(X)) | (~xuntil22(X))))),
% 1.90/1.82 inference(bind,[status(th)],[])).
% 1.90/1.82 tff(13207,plain,
% 1.90/1.82 (![X: $i] : (loop | (~last(X)) | (~xuntil22(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(quant_intro,[status(thm)],[13206])).
% 1.90/1.82 tff(13208,plain,
% 1.90/1.82 (![X: $i] : (loop | (~last(X)) | (~xuntil22(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13209,plain,
% 1.90/1.82 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil22(X))) <=> (loop | (~last(X)) | (~xuntil22(X))))),
% 1.90/1.82 inference(bind,[status(th)],[])).
% 1.90/1.82 tff(13210,plain,
% 1.90/1.82 (![X: $i] : ((loop | (~last(X))) | (~xuntil22(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(quant_intro,[status(thm)],[13209])).
% 1.90/1.82 tff(13211,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil22(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 1.90/1.82 tff(13212,plain,
% 1.90/1.82 (![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13211, 13210])).
% 1.90/1.82 tff(13213,plain,
% 1.90/1.82 (![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13212, 13208])).
% 1.90/1.82 tff(13214,plain,(
% 1.90/1.82 ![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(skolemize,[status(sab)],[13213])).
% 1.90/1.82 tff(13215,plain,
% 1.90/1.82 (![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13214, 13207])).
% 1.90/1.82 tff(13216,plain,
% 1.90/1.82 (((~![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))) | (loop | (~last(s104)) | (~xuntil22(s104)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))) | loop | (~last(s104)) | (~xuntil22(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13217,plain,
% 1.90/1.82 ((~![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))) | (loop | (~last(s104)) | (~xuntil22(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13218,plain,
% 1.90/1.82 ((~![X: $i] : (loop | (~last(X)) | (~xuntil22(X)))) | loop | (~last(s104)) | (~xuntil22(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13217, 13216])).
% 1.90/1.82 tff(13219,plain,
% 1.90/1.82 (loop | (~xuntil22(s104))),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13218, 10853, 13215])).
% 1.90/1.82 tff(13220,plain,
% 1.90/1.82 (~xuntil22(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13219, 13205])).
% 1.90/1.82 tff(13221,plain,
% 1.90/1.82 (node20(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[10842, 13220])).
% 1.90/1.82 tff(13222,plain,
% 1.90/1.82 (^[X: $i] : refl((loop | (~always19(X)) | (~last(X))) <=> (loop | (~always19(X)) | (~last(X))))),
% 1.90/1.82 inference(bind,[status(th)],[])).
% 1.90/1.82 tff(13223,plain,
% 1.90/1.82 (![X: $i] : (loop | (~always19(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(quant_intro,[status(thm)],[13222])).
% 1.90/1.82 tff(13224,plain,
% 1.90/1.82 (![X: $i] : (loop | (~always19(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13225,plain,
% 1.90/1.82 (^[X: $i] : rewrite(((loop | (~always19(X))) | (~last(X))) <=> (loop | (~always19(X)) | (~last(X))))),
% 1.90/1.82 inference(bind,[status(th)],[])).
% 1.90/1.82 tff(13226,plain,
% 1.90/1.82 (![X: $i] : ((loop | (~always19(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(quant_intro,[status(thm)],[13225])).
% 1.90/1.82 tff(13227,axiom,(![X: $i] : ((loop | (~always19(X))) | (~last(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 1.90/1.82 tff(13228,plain,
% 1.90/1.82 (![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13227, 13226])).
% 1.90/1.82 tff(13229,plain,
% 1.90/1.82 (![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13228, 13224])).
% 1.90/1.82 tff(13230,plain,(
% 1.90/1.82 ![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(skolemize,[status(sab)],[13229])).
% 1.90/1.82 tff(13231,plain,
% 1.90/1.82 (![X: $i] : (loop | (~always19(X)) | (~last(X)))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13230, 13223])).
% 1.90/1.82 tff(13232,plain,
% 1.90/1.82 (((~![X: $i] : (loop | (~always19(X)) | (~last(X)))) | (loop | (~always19(s104)) | (~last(s104)))) <=> ((~![X: $i] : (loop | (~always19(X)) | (~last(X)))) | loop | (~always19(s104)) | (~last(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13233,plain,
% 1.90/1.82 ((~![X: $i] : (loop | (~always19(X)) | (~last(X)))) | (loop | (~always19(s104)) | (~last(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13234,plain,
% 1.90/1.82 ((~![X: $i] : (loop | (~always19(X)) | (~last(X)))) | loop | (~always19(s104)) | (~last(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13233, 13232])).
% 1.90/1.82 tff(13235,plain,
% 1.90/1.82 (loop | (~always19(s104))),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13234, 10853, 13231])).
% 1.90/1.82 tff(13236,plain,
% 1.90/1.82 (~always19(s104)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13235, 13205])).
% 1.90/1.82 tff(13237,plain,
% 1.90/1.82 (((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s104) | (~node20(s104)))) <=> ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s104) | (~node20(s104)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13238,plain,
% 1.90/1.82 ((~![X: $i] : (always19(X) | (~node20(X)))) | (always19(s104) | (~node20(s104)))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13239,plain,
% 1.90/1.82 ((~![X: $i] : (always19(X) | (~node20(X)))) | always19(s104) | (~node20(s104))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13238, 13237])).
% 1.90/1.82 tff(13240,plain,
% 1.90/1.82 ($false),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13239, 8579, 13236, 13221])).
% 1.90/1.82 tff(13241,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 1.90/1.82 tff(13242,assumption,(~until2p23(s4)), introduced(assumption)).
% 1.90/1.82 tff(13243,assumption,(trans(s104, s4)), introduced(assumption)).
% 1.90/1.82 tff(13244,plain,
% 1.90/1.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13245,plain,
% 1.90/1.82 (((~trans(s104, s4)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s4)) <=> (until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4)))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13246,plain,
% 1.90/1.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s4)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4))))),
% 1.90/1.82 inference(monotonicity,[status(thm)],[13245])).
% 1.90/1.82 tff(13247,plain,
% 1.90/1.82 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s4)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4)))),
% 1.90/1.82 inference(transitivity,[status(thm)],[13246, 13244])).
% 1.90/1.82 tff(13248,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s4)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s4))),
% 1.90/1.82 inference(quant_inst,[status(thm)],[])).
% 1.90/1.82 tff(13249,plain,
% 1.90/1.82 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s4) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s4))),
% 1.90/1.82 inference(modus_ponens,[status(thm)],[13248, 13247])).
% 1.90/1.82 tff(13250,plain,
% 1.90/1.82 ($false),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13249, 10853, 13243, 11532, 13242, 11533])).
% 1.90/1.82 tff(13251,plain,((~trans(s104, s4)) | until2p23(s4) | (~xuntil22(s104))), inference(lemma,lemma(discharge,[]))).
% 1.90/1.82 tff(13252,plain,
% 1.90/1.82 (~trans(s104, s4)),
% 1.90/1.82 inference(unit_resolution,[status(thm)],[13251, 12256, 10843])).
% 1.90/1.82 tff(13253,plain,
% 1.90/1.82 (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104))),
% 1.90/1.82 inference(rewrite,[status(thm)],[])).
% 1.90/1.82 tff(13254,plain,
% 1.90/1.82 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)) | trans(s104, s104)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104))),
% 1.90/1.83 inference(rewrite,[status(thm)],[])).
% 1.90/1.83 tff(13255,plain,
% 1.90/1.83 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102)) | trans(s104, s103)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103))),
% 1.91/1.83 inference(rewrite,[status(thm)],[])).
% 1.91/1.83 tff(13256,plain,
% 1.91/1.83 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101)) | trans(s104, s102)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102))),
% 1.91/1.84 inference(rewrite,[status(thm)],[])).
% 1.91/1.84 tff(13257,plain,
% 1.91/1.84 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100)) | trans(s104, s101)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101))),
% 1.91/1.84 inference(rewrite,[status(thm)],[])).
% 1.91/1.84 tff(13258,plain,
% 1.91/1.84 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99)) | trans(s104, s100)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100))),
% 1.91/1.84 inference(rewrite,[status(thm)],[])).
% 1.91/1.84 tff(13259,plain,
% 1.91/1.84 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98)) | trans(s104, s99)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99))),
% 1.91/1.85 inference(rewrite,[status(thm)],[])).
% 1.91/1.85 tff(13260,plain,
% 1.91/1.85 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97)) | trans(s104, s98)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98))),
% 1.91/1.85 inference(rewrite,[status(thm)],[])).
% 1.91/1.85 tff(13261,plain,
% 1.91/1.85 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96)) | trans(s104, s97)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97))),
% 1.91/1.85 inference(rewrite,[status(thm)],[])).
% 1.91/1.85 tff(13262,plain,
% 1.91/1.85 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95)) | trans(s104, s96)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96))),
% 1.91/1.86 inference(rewrite,[status(thm)],[])).
% 1.91/1.86 tff(13263,plain,
% 1.91/1.86 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94)) | trans(s104, s95)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95))),
% 1.91/1.86 inference(rewrite,[status(thm)],[])).
% 1.91/1.86 tff(13264,plain,
% 1.91/1.86 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93)) | trans(s104, s94)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94))),
% 1.91/1.86 inference(rewrite,[status(thm)],[])).
% 1.91/1.86 tff(13265,plain,
% 1.91/1.86 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92)) | trans(s104, s93)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93))),
% 1.91/1.86 inference(rewrite,[status(thm)],[])).
% 1.91/1.86 tff(13266,plain,
% 1.91/1.86 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91)) | trans(s104, s92)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92))),
% 1.91/1.87 inference(rewrite,[status(thm)],[])).
% 1.91/1.87 tff(13267,plain,
% 1.91/1.87 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90)) | trans(s104, s91)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91))),
% 1.91/1.87 inference(rewrite,[status(thm)],[])).
% 1.91/1.87 tff(13268,plain,
% 1.91/1.87 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89)) | trans(s104, s90)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90))),
% 1.91/1.87 inference(rewrite,[status(thm)],[])).
% 1.91/1.87 tff(13269,plain,
% 1.91/1.87 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88)) | trans(s104, s89)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89))),
% 1.91/1.87 inference(rewrite,[status(thm)],[])).
% 1.91/1.87 tff(13270,plain,
% 1.91/1.87 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87)) | trans(s104, s88)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88))),
% 1.91/1.88 inference(rewrite,[status(thm)],[])).
% 1.91/1.88 tff(13271,plain,
% 1.91/1.88 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86)) | trans(s104, s87)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87))),
% 1.91/1.88 inference(rewrite,[status(thm)],[])).
% 1.91/1.88 tff(13272,plain,
% 1.91/1.88 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85)) | trans(s104, s86)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86))),
% 1.91/1.88 inference(rewrite,[status(thm)],[])).
% 1.91/1.88 tff(13273,plain,
% 1.91/1.88 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84)) | trans(s104, s85)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85))),
% 1.91/1.88 inference(rewrite,[status(thm)],[])).
% 1.91/1.88 tff(13274,plain,
% 1.91/1.88 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83)) | trans(s104, s84)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84))),
% 1.91/1.89 inference(rewrite,[status(thm)],[])).
% 1.91/1.89 tff(13275,plain,
% 1.91/1.89 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82)) | trans(s104, s83)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83))),
% 1.91/1.89 inference(rewrite,[status(thm)],[])).
% 1.91/1.89 tff(13276,plain,
% 1.91/1.89 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81)) | trans(s104, s82)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82))),
% 1.91/1.89 inference(rewrite,[status(thm)],[])).
% 1.91/1.89 tff(13277,plain,
% 1.91/1.89 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80)) | trans(s104, s81)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81))),
% 1.91/1.90 inference(rewrite,[status(thm)],[])).
% 1.91/1.90 tff(13278,plain,
% 1.91/1.90 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79)) | trans(s104, s80)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80))),
% 1.91/1.90 inference(rewrite,[status(thm)],[])).
% 1.91/1.90 tff(13279,plain,
% 1.91/1.90 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78)) | trans(s104, s79)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79))),
% 1.91/1.90 inference(rewrite,[status(thm)],[])).
% 1.91/1.90 tff(13280,plain,
% 1.91/1.90 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77)) | trans(s104, s78)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78))),
% 1.91/1.90 inference(rewrite,[status(thm)],[])).
% 1.91/1.90 tff(13281,plain,
% 1.91/1.90 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76)) | trans(s104, s77)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77))),
% 1.91/1.91 inference(rewrite,[status(thm)],[])).
% 1.91/1.91 tff(13282,plain,
% 1.91/1.91 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75)) | trans(s104, s76)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76))),
% 1.91/1.91 inference(rewrite,[status(thm)],[])).
% 1.91/1.91 tff(13283,plain,
% 1.91/1.91 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74)) | trans(s104, s75)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75))),
% 1.91/1.91 inference(rewrite,[status(thm)],[])).
% 1.91/1.91 tff(13284,plain,
% 1.91/1.91 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73)) | trans(s104, s74)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74))),
% 2.00/1.91 inference(rewrite,[status(thm)],[])).
% 2.00/1.91 tff(13285,plain,
% 2.00/1.91 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72)) | trans(s104, s73)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73))),
% 2.00/1.92 inference(rewrite,[status(thm)],[])).
% 2.00/1.92 tff(13286,plain,
% 2.00/1.92 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71)) | trans(s104, s72)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72))),
% 2.00/1.92 inference(rewrite,[status(thm)],[])).
% 2.00/1.92 tff(13287,plain,
% 2.00/1.92 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70)) | trans(s104, s71)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71))),
% 2.00/1.92 inference(rewrite,[status(thm)],[])).
% 2.00/1.92 tff(13288,plain,
% 2.00/1.92 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69)) | trans(s104, s70)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70))),
% 2.00/1.92 inference(rewrite,[status(thm)],[])).
% 2.00/1.92 tff(13289,plain,
% 2.00/1.92 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68)) | trans(s104, s69)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69))),
% 2.00/1.92 inference(rewrite,[status(thm)],[])).
% 2.00/1.92 tff(13290,plain,
% 2.00/1.92 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67)) | trans(s104, s68)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68))),
% 2.00/1.93 inference(rewrite,[status(thm)],[])).
% 2.00/1.93 tff(13291,plain,
% 2.00/1.93 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66)) | trans(s104, s67)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67))),
% 2.00/1.93 inference(rewrite,[status(thm)],[])).
% 2.00/1.93 tff(13292,plain,
% 2.00/1.93 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65)) | trans(s104, s66)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66))),
% 2.00/1.93 inference(rewrite,[status(thm)],[])).
% 2.00/1.93 tff(13293,plain,
% 2.00/1.93 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64)) | trans(s104, s65)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65))),
% 2.00/1.93 inference(rewrite,[status(thm)],[])).
% 2.00/1.93 tff(13294,plain,
% 2.00/1.93 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63)) | trans(s104, s64)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64))),
% 2.00/1.93 inference(rewrite,[status(thm)],[])).
% 2.00/1.93 tff(13295,plain,
% 2.00/1.93 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62)) | trans(s104, s63)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63))),
% 2.00/1.94 inference(rewrite,[status(thm)],[])).
% 2.00/1.94 tff(13296,plain,
% 2.00/1.94 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61)) | trans(s104, s62)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62))),
% 2.00/1.94 inference(rewrite,[status(thm)],[])).
% 2.00/1.94 tff(13297,plain,
% 2.00/1.94 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60)) | trans(s104, s61)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61))),
% 2.00/1.94 inference(rewrite,[status(thm)],[])).
% 2.00/1.94 tff(13298,plain,
% 2.00/1.94 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59)) | trans(s104, s60)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60))),
% 2.00/1.94 inference(rewrite,[status(thm)],[])).
% 2.00/1.94 tff(13299,plain,
% 2.00/1.94 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58)) | trans(s104, s59)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59))),
% 2.00/1.94 inference(rewrite,[status(thm)],[])).
% 2.00/1.94 tff(13300,plain,
% 2.00/1.94 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57)) | trans(s104, s58)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58))),
% 2.00/1.95 inference(rewrite,[status(thm)],[])).
% 2.00/1.95 tff(13301,plain,
% 2.00/1.95 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56)) | trans(s104, s57)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57))),
% 2.00/1.95 inference(rewrite,[status(thm)],[])).
% 2.00/1.95 tff(13302,plain,
% 2.00/1.95 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55)) | trans(s104, s56)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56))),
% 2.00/1.95 inference(rewrite,[status(thm)],[])).
% 2.00/1.95 tff(13303,plain,
% 2.00/1.95 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54)) | trans(s104, s55)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55))),
% 2.00/1.95 inference(rewrite,[status(thm)],[])).
% 2.00/1.95 tff(13304,plain,
% 2.00/1.95 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53)) | trans(s104, s54)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54))),
% 2.00/1.95 inference(rewrite,[status(thm)],[])).
% 2.00/1.95 tff(13305,plain,
% 2.00/1.95 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52)) | trans(s104, s53)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13306,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51)) | trans(s104, s52)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13307,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50)) | trans(s104, s51)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13308,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49)) | trans(s104, s50)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13309,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48)) | trans(s104, s49)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13310,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47)) | trans(s104, s48)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48))),
% 2.00/1.96 inference(rewrite,[status(thm)],[])).
% 2.00/1.96 tff(13311,plain,
% 2.00/1.96 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46)) | trans(s104, s47)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13312,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45)) | trans(s104, s46)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13313,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44)) | trans(s104, s45)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13314,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43)) | trans(s104, s44)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13315,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42)) | trans(s104, s43)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13316,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41)) | trans(s104, s42)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13317,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40)) | trans(s104, s41)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41))),
% 2.00/1.97 inference(rewrite,[status(thm)],[])).
% 2.00/1.97 tff(13318,plain,
% 2.00/1.97 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39)) | trans(s104, s40)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13319,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38)) | trans(s104, s39)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13320,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37)) | trans(s104, s38)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13321,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36)) | trans(s104, s37)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13322,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35)) | trans(s104, s36)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13323,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34)) | trans(s104, s35)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35))),
% 2.00/1.98 inference(rewrite,[status(thm)],[])).
% 2.00/1.98 tff(13324,plain,
% 2.00/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33)) | trans(s104, s34)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34))),
% 2.06/1.98 inference(rewrite,[status(thm)],[])).
% 2.06/1.98 tff(13325,plain,
% 2.06/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32)) | trans(s104, s33)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33))),
% 2.06/1.98 inference(rewrite,[status(thm)],[])).
% 2.06/1.98 tff(13326,plain,
% 2.06/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31)) | trans(s104, s32)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32))),
% 2.06/1.98 inference(rewrite,[status(thm)],[])).
% 2.06/1.98 tff(13327,plain,
% 2.06/1.98 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30)) | trans(s104, s31)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13328,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29)) | trans(s104, s30)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13329,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28)) | trans(s104, s29)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13330,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27)) | trans(s104, s28)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13331,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26)) | trans(s104, s27)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13332,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25)) | trans(s104, s26)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13333,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24)) | trans(s104, s25)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13334,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23)) | trans(s104, s24)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13335,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22)) | trans(s104, s23)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13336,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21)) | trans(s104, s22)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13337,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20)) | trans(s104, s21)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21))),
% 2.06/1.99 inference(rewrite,[status(thm)],[])).
% 2.06/1.99 tff(13338,plain,
% 2.06/1.99 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19)) | trans(s104, s20)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13339,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18)) | trans(s104, s19)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13340,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17)) | trans(s104, s18)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13341,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16)) | trans(s104, s17)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13342,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15)) | trans(s104, s16)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13343,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14)) | trans(s104, s15)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13344,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13)) | trans(s104, s14)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13345,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12)) | trans(s104, s13)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13346,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11)) | trans(s104, s12)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13347,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10)) | trans(s104, s11)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13348,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9)) | trans(s104, s10)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13349,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8)) | trans(s104, s9)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13350,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7)) | trans(s104, s8)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13351,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6)) | trans(s104, s7)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13352,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5)) | trans(s104, s6)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13353,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4)) | trans(s104, s5)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13354,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3)) | trans(s104, s4)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13355,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2)) | trans(s104, s3)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13356,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0) | trans(s104, s1)) | trans(s104, s2)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13357,plain,
% 2.06/2.00 ((((~loop) | trans(s104, s0)) | trans(s104, s1)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1))),
% 2.06/2.00 inference(rewrite,[status(thm)],[])).
% 2.06/2.00 tff(13358,plain,
% 2.06/2.00 (((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1)) | trans(s104, s2))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13357])).
% 2.06/2.00 tff(13359,plain,
% 2.06/2.00 (((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13358, 13356])).
% 2.06/2.00 tff(13360,plain,
% 2.06/2.00 ((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2)) | trans(s104, s3))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13359])).
% 2.06/2.00 tff(13361,plain,
% 2.06/2.00 ((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13360, 13355])).
% 2.06/2.00 tff(13362,plain,
% 2.06/2.00 (((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3)) | trans(s104, s4))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13361])).
% 2.06/2.00 tff(13363,plain,
% 2.06/2.00 (((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13362, 13354])).
% 2.06/2.00 tff(13364,plain,
% 2.06/2.00 ((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4)) | trans(s104, s5))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13363])).
% 2.06/2.00 tff(13365,plain,
% 2.06/2.00 ((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13364, 13353])).
% 2.06/2.00 tff(13366,plain,
% 2.06/2.00 (((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5)) | trans(s104, s6))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13365])).
% 2.06/2.00 tff(13367,plain,
% 2.06/2.00 (((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13366, 13352])).
% 2.06/2.00 tff(13368,plain,
% 2.06/2.00 ((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6)) | trans(s104, s7))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13367])).
% 2.06/2.00 tff(13369,plain,
% 2.06/2.00 ((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13368, 13351])).
% 2.06/2.00 tff(13370,plain,
% 2.06/2.00 (((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7)) | trans(s104, s8))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13369])).
% 2.06/2.00 tff(13371,plain,
% 2.06/2.00 (((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13370, 13350])).
% 2.06/2.00 tff(13372,plain,
% 2.06/2.00 ((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8)) | trans(s104, s9))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13371])).
% 2.06/2.00 tff(13373,plain,
% 2.06/2.00 ((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13372, 13349])).
% 2.06/2.00 tff(13374,plain,
% 2.06/2.00 (((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9)) | trans(s104, s10))),
% 2.06/2.00 inference(monotonicity,[status(thm)],[13373])).
% 2.06/2.00 tff(13375,plain,
% 2.06/2.00 (((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10))),
% 2.06/2.00 inference(transitivity,[status(thm)],[13374, 13348])).
% 2.06/2.00 tff(13376,plain,
% 2.06/2.00 ((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10)) | trans(s104, s11))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13375])).
% 2.06/2.01 tff(13377,plain,
% 2.06/2.01 ((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13376, 13347])).
% 2.06/2.01 tff(13378,plain,
% 2.06/2.01 (((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11)) | trans(s104, s12))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13377])).
% 2.06/2.01 tff(13379,plain,
% 2.06/2.01 (((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13378, 13346])).
% 2.06/2.01 tff(13380,plain,
% 2.06/2.01 ((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12)) | trans(s104, s13))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13379])).
% 2.06/2.01 tff(13381,plain,
% 2.06/2.01 ((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13380, 13345])).
% 2.06/2.01 tff(13382,plain,
% 2.06/2.01 (((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13)) | trans(s104, s14))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13381])).
% 2.06/2.01 tff(13383,plain,
% 2.06/2.01 (((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13382, 13344])).
% 2.06/2.01 tff(13384,plain,
% 2.06/2.01 ((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14)) | trans(s104, s15))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13383])).
% 2.06/2.01 tff(13385,plain,
% 2.06/2.01 ((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13384, 13343])).
% 2.06/2.01 tff(13386,plain,
% 2.06/2.01 (((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15)) | trans(s104, s16))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13385])).
% 2.06/2.01 tff(13387,plain,
% 2.06/2.01 (((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13386, 13342])).
% 2.06/2.01 tff(13388,plain,
% 2.06/2.01 ((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16)) | trans(s104, s17))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13387])).
% 2.06/2.01 tff(13389,plain,
% 2.06/2.01 ((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13388, 13341])).
% 2.06/2.01 tff(13390,plain,
% 2.06/2.01 (((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17)) | trans(s104, s18))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13389])).
% 2.06/2.01 tff(13391,plain,
% 2.06/2.01 (((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18))),
% 2.06/2.01 inference(transitivity,[status(thm)],[13390, 13340])).
% 2.06/2.01 tff(13392,plain,
% 2.06/2.01 ((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18)) | trans(s104, s19))),
% 2.06/2.01 inference(monotonicity,[status(thm)],[13391])).
% 2.06/2.01 tff(13393,plain,
% 2.06/2.01 ((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13392, 13339])).
% 2.06/2.02 tff(13394,plain,
% 2.06/2.02 (((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19)) | trans(s104, s20))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13393])).
% 2.06/2.02 tff(13395,plain,
% 2.06/2.02 (((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13394, 13338])).
% 2.06/2.02 tff(13396,plain,
% 2.06/2.02 ((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20)) | trans(s104, s21))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13395])).
% 2.06/2.02 tff(13397,plain,
% 2.06/2.02 ((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13396, 13337])).
% 2.06/2.02 tff(13398,plain,
% 2.06/2.02 (((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21)) | trans(s104, s22))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13397])).
% 2.06/2.02 tff(13399,plain,
% 2.06/2.02 (((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13398, 13336])).
% 2.06/2.02 tff(13400,plain,
% 2.06/2.02 ((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22)) | trans(s104, s23))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13399])).
% 2.06/2.02 tff(13401,plain,
% 2.06/2.02 ((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13400, 13335])).
% 2.06/2.02 tff(13402,plain,
% 2.06/2.02 (((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23)) | trans(s104, s24))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13401])).
% 2.06/2.02 tff(13403,plain,
% 2.06/2.02 (((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24))),
% 2.06/2.02 inference(transitivity,[status(thm)],[13402, 13334])).
% 2.06/2.02 tff(13404,plain,
% 2.06/2.02 ((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24)) | trans(s104, s25))),
% 2.06/2.02 inference(monotonicity,[status(thm)],[13403])).
% 2.06/2.02 tff(13405,plain,
% 2.06/2.02 ((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13404, 13333])).
% 2.06/2.03 tff(13406,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25)) | trans(s104, s26))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13405])).
% 2.06/2.03 tff(13407,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13406, 13332])).
% 2.06/2.03 tff(13408,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26)) | trans(s104, s27))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13407])).
% 2.06/2.03 tff(13409,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13408, 13331])).
% 2.06/2.03 tff(13410,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27)) | trans(s104, s28))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13409])).
% 2.06/2.03 tff(13411,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13410, 13330])).
% 2.06/2.03 tff(13412,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28)) | trans(s104, s29))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13411])).
% 2.06/2.03 tff(13413,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13412, 13329])).
% 2.06/2.03 tff(13414,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29)) | trans(s104, s30))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13413])).
% 2.06/2.03 tff(13415,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13414, 13328])).
% 2.06/2.03 tff(13416,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30)) | trans(s104, s31))),
% 2.06/2.03 inference(monotonicity,[status(thm)],[13415])).
% 2.06/2.03 tff(13417,plain,
% 2.06/2.03 ((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31))),
% 2.06/2.03 inference(transitivity,[status(thm)],[13416, 13327])).
% 2.06/2.03 tff(13418,plain,
% 2.06/2.03 (((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31)) | trans(s104, s32))),
% 2.06/2.04 inference(monotonicity,[status(thm)],[13417])).
% 2.06/2.04 tff(13419,plain,
% 2.06/2.04 (((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32))),
% 2.06/2.04 inference(transitivity,[status(thm)],[13418, 13326])).
% 2.06/2.04 tff(13420,plain,
% 2.06/2.04 ((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32)) | trans(s104, s33))),
% 2.06/2.04 inference(monotonicity,[status(thm)],[13419])).
% 2.06/2.04 tff(13421,plain,
% 2.06/2.04 ((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33))),
% 2.06/2.04 inference(transitivity,[status(thm)],[13420, 13325])).
% 2.06/2.04 tff(13422,plain,
% 2.06/2.04 (((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33)) | trans(s104, s34))),
% 2.06/2.04 inference(monotonicity,[status(thm)],[13421])).
% 2.06/2.04 tff(13423,plain,
% 2.06/2.04 (((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34))),
% 2.06/2.04 inference(transitivity,[status(thm)],[13422, 13324])).
% 2.06/2.04 tff(13424,plain,
% 2.06/2.04 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34)) | trans(s104, s35))),
% 2.06/2.04 inference(monotonicity,[status(thm)],[13423])).
% 2.06/2.04 tff(13425,plain,
% 2.06/2.04 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35))),
% 2.06/2.04 inference(transitivity,[status(thm)],[13424, 13323])).
% 2.06/2.04 tff(13426,plain,
% 2.06/2.04 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35)) | trans(s104, s36))),
% 2.06/2.05 inference(monotonicity,[status(thm)],[13425])).
% 2.06/2.05 tff(13427,plain,
% 2.06/2.05 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36))),
% 2.06/2.05 inference(transitivity,[status(thm)],[13426, 13322])).
% 2.06/2.05 tff(13428,plain,
% 2.06/2.05 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36)) | trans(s104, s37))),
% 2.06/2.05 inference(monotonicity,[status(thm)],[13427])).
% 2.06/2.05 tff(13429,plain,
% 2.06/2.05 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37))),
% 2.06/2.05 inference(transitivity,[status(thm)],[13428, 13321])).
% 2.06/2.05 tff(13430,plain,
% 2.06/2.05 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37)) | trans(s104, s38))),
% 2.06/2.05 inference(monotonicity,[status(thm)],[13429])).
% 2.06/2.05 tff(13431,plain,
% 2.06/2.05 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38))),
% 2.06/2.05 inference(transitivity,[status(thm)],[13430, 13320])).
% 2.06/2.05 tff(13432,plain,
% 2.06/2.05 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38)) | trans(s104, s39))),
% 2.06/2.05 inference(monotonicity,[status(thm)],[13431])).
% 2.06/2.05 tff(13433,plain,
% 2.06/2.05 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39))),
% 2.06/2.05 inference(transitivity,[status(thm)],[13432, 13319])).
% 2.06/2.05 tff(13434,plain,
% 2.06/2.05 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39)) | trans(s104, s40))),
% 2.06/2.06 inference(monotonicity,[status(thm)],[13433])).
% 2.06/2.06 tff(13435,plain,
% 2.06/2.06 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40))),
% 2.06/2.06 inference(transitivity,[status(thm)],[13434, 13318])).
% 2.06/2.06 tff(13436,plain,
% 2.06/2.06 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40)) | trans(s104, s41))),
% 2.06/2.06 inference(monotonicity,[status(thm)],[13435])).
% 2.06/2.06 tff(13437,plain,
% 2.06/2.06 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41))),
% 2.06/2.06 inference(transitivity,[status(thm)],[13436, 13317])).
% 2.06/2.06 tff(13438,plain,
% 2.06/2.06 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41)) | trans(s104, s42))),
% 2.06/2.06 inference(monotonicity,[status(thm)],[13437])).
% 2.15/2.06 tff(13439,plain,
% 2.15/2.06 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42))),
% 2.15/2.06 inference(transitivity,[status(thm)],[13438, 13316])).
% 2.15/2.06 tff(13440,plain,
% 2.15/2.06 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42)) | trans(s104, s43))),
% 2.15/2.06 inference(monotonicity,[status(thm)],[13439])).
% 2.15/2.06 tff(13441,plain,
% 2.15/2.06 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43))),
% 2.15/2.07 inference(transitivity,[status(thm)],[13440, 13315])).
% 2.15/2.07 tff(13442,plain,
% 2.15/2.07 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43)) | trans(s104, s44))),
% 2.15/2.07 inference(monotonicity,[status(thm)],[13441])).
% 2.15/2.07 tff(13443,plain,
% 2.15/2.07 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44))),
% 2.15/2.07 inference(transitivity,[status(thm)],[13442, 13314])).
% 2.15/2.07 tff(13444,plain,
% 2.15/2.07 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44)) | trans(s104, s45))),
% 2.15/2.07 inference(monotonicity,[status(thm)],[13443])).
% 2.15/2.07 tff(13445,plain,
% 2.15/2.07 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45))),
% 2.15/2.07 inference(transitivity,[status(thm)],[13444, 13313])).
% 2.15/2.07 tff(13446,plain,
% 2.15/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45)) | trans(s104, s46))),
% 2.15/2.07 inference(monotonicity,[status(thm)],[13445])).
% 2.15/2.07 tff(13447,plain,
% 2.15/2.07 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46))),
% 2.15/2.08 inference(transitivity,[status(thm)],[13446, 13312])).
% 2.15/2.08 tff(13448,plain,
% 2.15/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46)) | trans(s104, s47))),
% 2.15/2.08 inference(monotonicity,[status(thm)],[13447])).
% 2.15/2.08 tff(13449,plain,
% 2.15/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47))),
% 2.16/2.08 inference(transitivity,[status(thm)],[13448, 13311])).
% 2.16/2.08 tff(13450,plain,
% 2.16/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47)) | trans(s104, s48))),
% 2.16/2.08 inference(monotonicity,[status(thm)],[13449])).
% 2.16/2.08 tff(13451,plain,
% 2.16/2.08 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48))),
% 2.16/2.08 inference(transitivity,[status(thm)],[13450, 13310])).
% 2.16/2.08 tff(13452,plain,
% 2.16/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48)) | trans(s104, s49))),
% 2.16/2.08 inference(monotonicity,[status(thm)],[13451])).
% 2.16/2.08 tff(13453,plain,
% 2.16/2.08 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49))),
% 2.16/2.09 inference(transitivity,[status(thm)],[13452, 13309])).
% 2.16/2.09 tff(13454,plain,
% 2.16/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49)) | trans(s104, s50))),
% 2.16/2.09 inference(monotonicity,[status(thm)],[13453])).
% 2.16/2.09 tff(13455,plain,
% 2.16/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50))),
% 2.16/2.09 inference(transitivity,[status(thm)],[13454, 13308])).
% 2.16/2.09 tff(13456,plain,
% 2.16/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50)) | trans(s104, s51))),
% 2.16/2.09 inference(monotonicity,[status(thm)],[13455])).
% 2.16/2.09 tff(13457,plain,
% 2.16/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51))),
% 2.16/2.09 inference(transitivity,[status(thm)],[13456, 13307])).
% 2.16/2.09 tff(13458,plain,
% 2.16/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51)) | trans(s104, s52))),
% 2.16/2.09 inference(monotonicity,[status(thm)],[13457])).
% 2.16/2.09 tff(13459,plain,
% 2.16/2.09 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52))),
% 2.16/2.09 inference(transitivity,[status(thm)],[13458, 13306])).
% 2.16/2.09 tff(13460,plain,
% 2.16/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52)) | trans(s104, s53))),
% 2.16/2.09 inference(monotonicity,[status(thm)],[13459])).
% 2.16/2.09 tff(13461,plain,
% 2.16/2.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53))),
% 2.16/2.10 inference(transitivity,[status(thm)],[13460, 13305])).
% 2.16/2.10 tff(13462,plain,
% 2.16/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53)) | trans(s104, s54))),
% 2.16/2.10 inference(monotonicity,[status(thm)],[13461])).
% 2.16/2.10 tff(13463,plain,
% 2.16/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54))),
% 2.16/2.10 inference(transitivity,[status(thm)],[13462, 13304])).
% 2.16/2.10 tff(13464,plain,
% 2.16/2.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54)) | trans(s104, s55))),
% 2.16/2.10 inference(monotonicity,[status(thm)],[13463])).
% 2.16/2.10 tff(13465,plain,
% 2.16/2.10 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55))),
% 2.16/2.10 inference(transitivity,[status(thm)],[13464, 13303])).
% 2.16/2.10 tff(13466,plain,
% 2.16/2.10 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55)) | trans(s104, s56))),
% 2.16/2.11 inference(monotonicity,[status(thm)],[13465])).
% 2.16/2.11 tff(13467,plain,
% 2.16/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56))),
% 2.16/2.11 inference(transitivity,[status(thm)],[13466, 13302])).
% 2.16/2.11 tff(13468,plain,
% 2.16/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56)) | trans(s104, s57))),
% 2.16/2.11 inference(monotonicity,[status(thm)],[13467])).
% 2.16/2.11 tff(13469,plain,
% 2.16/2.11 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57))),
% 2.16/2.11 inference(transitivity,[status(thm)],[13468, 13301])).
% 2.16/2.11 tff(13470,plain,
% 2.19/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57)) | trans(s104, s58))),
% 2.19/2.11 inference(monotonicity,[status(thm)],[13469])).
% 2.19/2.11 tff(13471,plain,
% 2.19/2.11 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58))),
% 2.19/2.12 inference(transitivity,[status(thm)],[13470, 13300])).
% 2.19/2.12 tff(13472,plain,
% 2.19/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58)) | trans(s104, s59))),
% 2.19/2.12 inference(monotonicity,[status(thm)],[13471])).
% 2.19/2.12 tff(13473,plain,
% 2.19/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59))),
% 2.19/2.12 inference(transitivity,[status(thm)],[13472, 13299])).
% 2.19/2.12 tff(13474,plain,
% 2.19/2.12 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59)) | trans(s104, s60))),
% 2.19/2.12 inference(monotonicity,[status(thm)],[13473])).
% 2.19/2.12 tff(13475,plain,
% 2.19/2.12 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60))),
% 2.19/2.12 inference(transitivity,[status(thm)],[13474, 13298])).
% 2.19/2.12 tff(13476,plain,
% 2.19/2.12 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60)) | trans(s104, s61))),
% 2.19/2.13 inference(monotonicity,[status(thm)],[13475])).
% 2.19/2.13 tff(13477,plain,
% 2.19/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61))),
% 2.19/2.13 inference(transitivity,[status(thm)],[13476, 13297])).
% 2.19/2.13 tff(13478,plain,
% 2.19/2.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61)) | trans(s104, s62))),
% 2.21/2.13 inference(monotonicity,[status(thm)],[13477])).
% 2.21/2.13 tff(13479,plain,
% 2.21/2.13 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62))),
% 2.21/2.13 inference(transitivity,[status(thm)],[13478, 13296])).
% 2.21/2.13 tff(13480,plain,
% 2.21/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62)) | trans(s104, s63))),
% 2.21/2.13 inference(monotonicity,[status(thm)],[13479])).
% 2.21/2.13 tff(13481,plain,
% 2.21/2.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63))),
% 2.21/2.14 inference(transitivity,[status(thm)],[13480, 13295])).
% 2.21/2.14 tff(13482,plain,
% 2.21/2.14 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63)) | trans(s104, s64))),
% 2.21/2.14 inference(monotonicity,[status(thm)],[13481])).
% 2.21/2.14 tff(13483,plain,
% 2.21/2.14 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64))),
% 2.21/2.14 inference(transitivity,[status(thm)],[13482, 13294])).
% 2.21/2.14 tff(13484,plain,
% 2.21/2.14 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64)) | trans(s104, s65))),
% 2.21/2.14 inference(monotonicity,[status(thm)],[13483])).
% 2.21/2.14 tff(13485,plain,
% 2.21/2.14 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65))),
% 2.21/2.15 inference(transitivity,[status(thm)],[13484, 13293])).
% 2.21/2.15 tff(13486,plain,
% 2.21/2.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65)) | trans(s104, s66))),
% 2.21/2.15 inference(monotonicity,[status(thm)],[13485])).
% 2.21/2.15 tff(13487,plain,
% 2.21/2.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66))),
% 2.21/2.15 inference(transitivity,[status(thm)],[13486, 13292])).
% 2.21/2.15 tff(13488,plain,
% 2.21/2.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66)) | trans(s104, s67))),
% 2.21/2.15 inference(monotonicity,[status(thm)],[13487])).
% 2.21/2.15 tff(13489,plain,
% 2.21/2.15 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67))),
% 2.21/2.15 inference(transitivity,[status(thm)],[13488, 13291])).
% 2.21/2.15 tff(13490,plain,
% 2.21/2.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67)) | trans(s104, s68))),
% 2.21/2.15 inference(monotonicity,[status(thm)],[13489])).
% 2.21/2.15 tff(13491,plain,
% 2.21/2.15 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68))),
% 2.21/2.16 inference(transitivity,[status(thm)],[13490, 13290])).
% 2.21/2.16 tff(13492,plain,
% 2.21/2.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68)) | trans(s104, s69))),
% 2.21/2.16 inference(monotonicity,[status(thm)],[13491])).
% 2.21/2.16 tff(13493,plain,
% 2.21/2.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69))),
% 2.21/2.16 inference(transitivity,[status(thm)],[13492, 13289])).
% 2.21/2.16 tff(13494,plain,
% 2.21/2.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69)) | trans(s104, s70))),
% 2.21/2.16 inference(monotonicity,[status(thm)],[13493])).
% 2.21/2.16 tff(13495,plain,
% 2.21/2.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70))),
% 2.21/2.17 inference(transitivity,[status(thm)],[13494, 13288])).
% 2.21/2.17 tff(13496,plain,
% 2.21/2.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70)) | trans(s104, s71))),
% 2.21/2.17 inference(monotonicity,[status(thm)],[13495])).
% 2.21/2.17 tff(13497,plain,
% 2.21/2.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71))),
% 2.21/2.17 inference(transitivity,[status(thm)],[13496, 13287])).
% 2.21/2.17 tff(13498,plain,
% 2.21/2.17 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71)) | trans(s104, s72))),
% 2.21/2.17 inference(monotonicity,[status(thm)],[13497])).
% 2.21/2.17 tff(13499,plain,
% 2.21/2.17 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72))),
% 2.21/2.17 inference(transitivity,[status(thm)],[13498, 13286])).
% 2.21/2.17 tff(13500,plain,
% 2.21/2.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72)) | trans(s104, s73))),
% 2.21/2.18 inference(monotonicity,[status(thm)],[13499])).
% 2.21/2.18 tff(13501,plain,
% 2.21/2.18 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73))),
% 2.21/2.18 inference(transitivity,[status(thm)],[13500, 13285])).
% 2.21/2.18 tff(13502,plain,
% 2.21/2.18 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73)) | trans(s104, s74))),
% 2.21/2.18 inference(monotonicity,[status(thm)],[13501])).
% 2.21/2.18 tff(13503,plain,
% 2.21/2.18 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74))),
% 2.21/2.18 inference(transitivity,[status(thm)],[13502, 13284])).
% 2.21/2.18 tff(13504,plain,
% 2.21/2.18 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74)) | trans(s104, s75))),
% 2.21/2.19 inference(monotonicity,[status(thm)],[13503])).
% 2.21/2.19 tff(13505,plain,
% 2.21/2.19 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75))),
% 2.21/2.19 inference(transitivity,[status(thm)],[13504, 13283])).
% 2.21/2.19 tff(13506,plain,
% 2.21/2.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75)) | trans(s104, s76))),
% 2.21/2.19 inference(monotonicity,[status(thm)],[13505])).
% 2.21/2.19 tff(13507,plain,
% 2.21/2.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76))),
% 2.21/2.19 inference(transitivity,[status(thm)],[13506, 13282])).
% 2.21/2.19 tff(13508,plain,
% 2.21/2.20 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76)) | trans(s104, s77))),
% 2.21/2.20 inference(monotonicity,[status(thm)],[13507])).
% 2.21/2.20 tff(13509,plain,
% 2.21/2.20 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77))),
% 2.21/2.20 inference(transitivity,[status(thm)],[13508, 13281])).
% 2.21/2.20 tff(13510,plain,
% 2.21/2.20 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77)) | trans(s104, s78))),
% 2.21/2.20 inference(monotonicity,[status(thm)],[13509])).
% 2.21/2.20 tff(13511,plain,
% 2.21/2.20 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78))),
% 2.21/2.21 inference(transitivity,[status(thm)],[13510, 13280])).
% 2.21/2.21 tff(13512,plain,
% 2.21/2.21 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78)) | trans(s104, s79))),
% 2.21/2.21 inference(monotonicity,[status(thm)],[13511])).
% 2.21/2.21 tff(13513,plain,
% 2.21/2.21 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79))),
% 2.21/2.21 inference(transitivity,[status(thm)],[13512, 13279])).
% 2.21/2.21 tff(13514,plain,
% 2.21/2.21 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79)) | trans(s104, s80))),
% 2.21/2.21 inference(monotonicity,[status(thm)],[13513])).
% 2.21/2.21 tff(13515,plain,
% 2.21/2.21 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80))),
% 2.30/2.22 inference(transitivity,[status(thm)],[13514, 13278])).
% 2.30/2.22 tff(13516,plain,
% 2.30/2.22 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80)) | trans(s104, s81))),
% 2.30/2.22 inference(monotonicity,[status(thm)],[13515])).
% 2.30/2.22 tff(13517,plain,
% 2.30/2.22 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81))),
% 2.30/2.22 inference(transitivity,[status(thm)],[13516, 13277])).
% 2.30/2.22 tff(13518,plain,
% 2.30/2.22 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81)) | trans(s104, s82))),
% 2.30/2.22 inference(monotonicity,[status(thm)],[13517])).
% 2.30/2.22 tff(13519,plain,
% 2.30/2.22 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82))),
% 2.30/2.23 inference(transitivity,[status(thm)],[13518, 13276])).
% 2.30/2.23 tff(13520,plain,
% 2.30/2.23 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82)) | trans(s104, s83))),
% 2.30/2.23 inference(monotonicity,[status(thm)],[13519])).
% 2.30/2.23 tff(13521,plain,
% 2.30/2.23 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83))),
% 2.30/2.23 inference(transitivity,[status(thm)],[13520, 13275])).
% 2.30/2.23 tff(13522,plain,
% 2.30/2.23 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83)) | trans(s104, s84))),
% 2.30/2.24 inference(monotonicity,[status(thm)],[13521])).
% 2.30/2.24 tff(13523,plain,
% 2.30/2.24 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84))),
% 2.30/2.24 inference(transitivity,[status(thm)],[13522, 13274])).
% 2.30/2.24 tff(13524,plain,
% 2.30/2.24 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84)) | trans(s104, s85))),
% 2.30/2.24 inference(monotonicity,[status(thm)],[13523])).
% 2.30/2.24 tff(13525,plain,
% 2.30/2.24 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85))),
% 2.30/2.24 inference(transitivity,[status(thm)],[13524, 13273])).
% 2.30/2.24 tff(13526,plain,
% 2.30/2.24 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85)) | trans(s104, s86))),
% 2.30/2.24 inference(monotonicity,[status(thm)],[13525])).
% 2.30/2.24 tff(13527,plain,
% 2.30/2.24 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86))),
% 2.30/2.25 inference(transitivity,[status(thm)],[13526, 13272])).
% 2.30/2.25 tff(13528,plain,
% 2.30/2.25 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86)) | trans(s104, s87))),
% 2.30/2.25 inference(monotonicity,[status(thm)],[13527])).
% 2.30/2.25 tff(13529,plain,
% 2.30/2.25 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87))),
% 2.30/2.25 inference(transitivity,[status(thm)],[13528, 13271])).
% 2.30/2.25 tff(13530,plain,
% 2.30/2.25 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87)) | trans(s104, s88))),
% 2.30/2.26 inference(monotonicity,[status(thm)],[13529])).
% 2.30/2.26 tff(13531,plain,
% 2.30/2.26 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88))),
% 2.30/2.26 inference(transitivity,[status(thm)],[13530, 13270])).
% 2.30/2.26 tff(13532,plain,
% 2.30/2.26 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88)) | trans(s104, s89))),
% 2.30/2.26 inference(monotonicity,[status(thm)],[13531])).
% 2.30/2.26 tff(13533,plain,
% 2.30/2.26 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89))),
% 2.30/2.26 inference(transitivity,[status(thm)],[13532, 13269])).
% 2.30/2.26 tff(13534,plain,
% 2.30/2.26 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89)) | trans(s104, s90))),
% 2.30/2.27 inference(monotonicity,[status(thm)],[13533])).
% 2.30/2.27 tff(13535,plain,
% 2.30/2.27 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90))),
% 2.30/2.27 inference(transitivity,[status(thm)],[13534, 13268])).
% 2.30/2.27 tff(13536,plain,
% 2.30/2.27 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90)) | trans(s104, s91))),
% 2.30/2.27 inference(monotonicity,[status(thm)],[13535])).
% 2.30/2.27 tff(13537,plain,
% 2.30/2.27 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91))),
% 2.30/2.28 inference(transitivity,[status(thm)],[13536, 13267])).
% 2.30/2.28 tff(13538,plain,
% 2.30/2.28 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91)) | trans(s104, s92))),
% 2.30/2.28 inference(monotonicity,[status(thm)],[13537])).
% 2.30/2.28 tff(13539,plain,
% 2.30/2.28 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92))),
% 2.30/2.28 inference(transitivity,[status(thm)],[13538, 13266])).
% 2.30/2.28 tff(13540,plain,
% 2.30/2.28 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92)) | trans(s104, s93))),
% 2.30/2.29 inference(monotonicity,[status(thm)],[13539])).
% 2.30/2.29 tff(13541,plain,
% 2.30/2.29 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93))),
% 2.30/2.29 inference(transitivity,[status(thm)],[13540, 13265])).
% 2.30/2.29 tff(13542,plain,
% 2.30/2.29 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93)) | trans(s104, s94))),
% 2.30/2.29 inference(monotonicity,[status(thm)],[13541])).
% 2.30/2.29 tff(13543,plain,
% 2.30/2.29 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94))),
% 2.37/2.30 inference(transitivity,[status(thm)],[13542, 13264])).
% 2.37/2.30 tff(13544,plain,
% 2.37/2.30 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94)) | trans(s104, s95))),
% 2.37/2.30 inference(monotonicity,[status(thm)],[13543])).
% 2.37/2.30 tff(13545,plain,
% 2.37/2.30 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95))),
% 2.37/2.30 inference(transitivity,[status(thm)],[13544, 13263])).
% 2.37/2.30 tff(13546,plain,
% 2.37/2.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95)) | trans(s104, s96))),
% 2.37/2.31 inference(monotonicity,[status(thm)],[13545])).
% 2.37/2.31 tff(13547,plain,
% 2.37/2.31 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96))),
% 2.37/2.31 inference(transitivity,[status(thm)],[13546, 13262])).
% 2.37/2.31 tff(13548,plain,
% 2.37/2.31 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96)) | trans(s104, s97))),
% 2.37/2.31 inference(monotonicity,[status(thm)],[13547])).
% 2.37/2.31 tff(13549,plain,
% 2.37/2.31 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97))),
% 2.37/2.31 inference(transitivity,[status(thm)],[13548, 13261])).
% 2.37/2.31 tff(13550,plain,
% 2.37/2.31 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97)) | trans(s104, s98))),
% 2.37/2.32 inference(monotonicity,[status(thm)],[13549])).
% 2.37/2.32 tff(13551,plain,
% 2.37/2.32 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98))),
% 2.37/2.32 inference(transitivity,[status(thm)],[13550, 13260])).
% 2.37/2.32 tff(13552,plain,
% 2.37/2.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98)) | trans(s104, s99))),
% 2.37/2.32 inference(monotonicity,[status(thm)],[13551])).
% 2.37/2.32 tff(13553,plain,
% 2.37/2.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99))),
% 2.37/2.33 inference(transitivity,[status(thm)],[13552, 13259])).
% 2.37/2.33 tff(13554,plain,
% 2.37/2.33 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99)) | trans(s104, s100))),
% 2.37/2.33 inference(monotonicity,[status(thm)],[13553])).
% 2.37/2.33 tff(13555,plain,
% 2.37/2.33 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100))),
% 2.37/2.33 inference(transitivity,[status(thm)],[13554, 13258])).
% 2.37/2.33 tff(13556,plain,
% 2.37/2.33 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100)) | trans(s104, s101))),
% 2.37/2.33 inference(monotonicity,[status(thm)],[13555])).
% 2.37/2.33 tff(13557,plain,
% 2.37/2.33 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101))),
% 2.37/2.34 inference(transitivity,[status(thm)],[13556, 13257])).
% 2.37/2.34 tff(13558,plain,
% 2.37/2.34 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101)) | trans(s104, s102))),
% 2.37/2.34 inference(monotonicity,[status(thm)],[13557])).
% 2.37/2.34 tff(13559,plain,
% 2.37/2.34 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102))),
% 2.37/2.34 inference(transitivity,[status(thm)],[13558, 13256])).
% 2.37/2.35 tff(13560,plain,
% 2.37/2.35 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) | trans(s104, s103)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102)) | trans(s104, s103))),
% 2.37/2.35 inference(monotonicity,[status(thm)],[13559])).
% 2.37/2.35 tff(13561,plain,
% 2.37/2.35 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) | trans(s104, s103)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103))),
% 2.37/2.35 inference(transitivity,[status(thm)],[13560, 13255])).
% 2.37/2.35 tff(13562,plain,
% 2.37/2.35 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) | trans(s104, s103)) | trans(s104, s104)) <=> (((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)) | trans(s104, s104))),
% 2.37/2.36 inference(monotonicity,[status(thm)],[13561])).
% 2.37/2.36 tff(13563,plain,
% 2.37/2.36 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) | trans(s104, s103)) | trans(s104, s104)) <=> ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104))),
% 2.37/2.36 inference(transitivity,[status(thm)],[13562, 13254])).
% 2.37/2.36 tff(13564,axiom,((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s104, s0)) | trans(s104, s1)) | trans(s104, s2)) | trans(s104, s3)) | trans(s104, s4)) | trans(s104, s5)) | trans(s104, s6)) | trans(s104, s7)) | trans(s104, s8)) | trans(s104, s9)) | trans(s104, s10)) | trans(s104, s11)) | trans(s104, s12)) | trans(s104, s13)) | trans(s104, s14)) | trans(s104, s15)) | trans(s104, s16)) | trans(s104, s17)) | trans(s104, s18)) | trans(s104, s19)) | trans(s104, s20)) | trans(s104, s21)) | trans(s104, s22)) | trans(s104, s23)) | trans(s104, s24)) | trans(s104, s25)) | trans(s104, s26)) | trans(s104, s27)) | trans(s104, s28)) | trans(s104, s29)) | trans(s104, s30)) | trans(s104, s31)) | trans(s104, s32)) | trans(s104, s33)) | trans(s104, s34)) | trans(s104, s35)) | trans(s104, s36)) | trans(s104, s37)) | trans(s104, s38)) | trans(s104, s39)) | trans(s104, s40)) | trans(s104, s41)) | trans(s104, s42)) | trans(s104, s43)) | trans(s104, s44)) | trans(s104, s45)) | trans(s104, s46)) | trans(s104, s47)) | trans(s104, s48)) | trans(s104, s49)) | trans(s104, s50)) | trans(s104, s51)) | trans(s104, s52)) | trans(s104, s53)) | trans(s104, s54)) | trans(s104, s55)) | trans(s104, s56)) | trans(s104, s57)) | trans(s104, s58)) | trans(s104, s59)) | trans(s104, s60)) | trans(s104, s61)) | trans(s104, s62)) | trans(s104, s63)) | trans(s104, s64)) | trans(s104, s65)) | trans(s104, s66)) | trans(s104, s67)) | trans(s104, s68)) | trans(s104, s69)) | trans(s104, s70)) | trans(s104, s71)) | trans(s104, s72)) | trans(s104, s73)) | trans(s104, s74)) | trans(s104, s75)) | trans(s104, s76)) | trans(s104, s77)) | trans(s104, s78)) | trans(s104, s79)) | trans(s104, s80)) | trans(s104, s81)) | trans(s104, s82)) | trans(s104, s83)) | trans(s104, s84)) | trans(s104, s85)) | trans(s104, s86)) | trans(s104, s87)) | trans(s104, s88)) | trans(s104, s89)) | trans(s104, s90)) | trans(s104, s91)) | trans(s104, s92)) | trans(s104, s93)) | trans(s104, s94)) | trans(s104, s95)) | trans(s104, s96)) | trans(s104, s97)) | trans(s104, s98)) | trans(s104, s99)) | trans(s104, s100)) | trans(s104, s101)) | trans(s104, s102)) | trans(s104, s103)) | trans(s104, s104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound107')).
% 2.37/2.36 tff(13565,plain,
% 2.37/2.36 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.36 inference(modus_ponens,[status(thm)],[13564, 13563])).
% 2.37/2.36 tff(13566,plain,
% 2.37/2.36 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.36 inference(modus_ponens,[status(thm)],[13565, 13253])).
% 2.37/2.36 tff(13567,plain,
% 2.37/2.36 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13566, 13253])).
% 2.37/2.37 tff(13568,plain,
% 2.37/2.37 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13567, 13253])).
% 2.37/2.37 tff(13569,plain,
% 2.37/2.37 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13568, 13253])).
% 2.37/2.37 tff(13570,plain,
% 2.37/2.37 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13569, 13253])).
% 2.37/2.37 tff(13571,plain,
% 2.37/2.37 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13570, 13253])).
% 2.37/2.37 tff(13572,plain,
% 2.37/2.37 ((~loop) | trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s4) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s20) | trans(s104, s21) | trans(s104, s22) | trans(s104, s23) | trans(s104, s24) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s32) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s40) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s91) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103) | trans(s104, s104)),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13571, 13253])).
% 2.37/2.37 tff(13573,plain,
% 2.37/2.37 (trans(s104, s40)),
% 2.37/2.37 inference(unit_resolution,[status(thm)],[13572, 13252, 13241, 13204, 13055, 13044, 13033, 13022, 13011, 13000, 12989, 12978, 12967, 12956, 12945, 12934, 12923, 12912, 12901, 12890, 12879, 12868, 12857, 12846, 12835, 12824, 12813, 12802, 12791, 12780, 12769, 12758, 12747, 12736, 12725, 12714, 12693, 12682, 12671, 12660, 12649, 12638, 12627, 12616, 12605, 12594, 12583, 12572, 12561, 12550, 12539, 12528, 12517, 12506, 12495, 12484, 12473, 12462, 12451, 12440, 12429, 12418, 12407, 12396, 12385, 12374, 12353, 12342, 12331, 12320, 12309, 12298, 12287, 12206, 12195, 12184, 12173, 12162, 12151, 12140, 12119, 12108, 12097, 12086, 12075, 12064, 12053, 12042, 12031, 12020, 12009, 11998, 11987, 11876, 11865, 11854, 11843, 11832, 11821, 11810, 11799, 11788, 11757, 11726, 11635, 11544])).
% 2.37/2.37 tff(13574,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40)))),
% 2.37/2.37 inference(rewrite,[status(thm)],[])).
% 2.37/2.37 tff(13575,plain,
% 2.37/2.37 (((~trans(s104, s40)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s40)) <=> (until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40)))),
% 2.37/2.37 inference(rewrite,[status(thm)],[])).
% 2.37/2.37 tff(13576,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s40)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | (until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40))))),
% 2.37/2.37 inference(monotonicity,[status(thm)],[13575])).
% 2.37/2.37 tff(13577,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s40)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40)))),
% 2.37/2.37 inference(transitivity,[status(thm)],[13576, 13574])).
% 2.37/2.37 tff(13578,plain,
% 2.37/2.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | ((~trans(s104, s40)) | (~last(s104)) | (~xuntil22(s104)) | until2p23(s40))),
% 2.37/2.37 inference(quant_inst,[status(thm)],[])).
% 2.37/2.37 tff(13579,plain,
% 2.37/2.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~last(X)) | (~xuntil22(X)) | until2p23(Y))) | until2p23(s40) | (~last(s104)) | (~xuntil22(s104)) | (~trans(s104, s40))),
% 2.37/2.37 inference(modus_ponens,[status(thm)],[13578, 13577])).
% 2.37/2.37 tff(13580,plain,
% 2.37/2.37 ($false),
% 2.37/2.37 inference(unit_resolution,[status(thm)],[13579, 10853, 13573, 11532, 11522, 10843])).
% 2.37/2.37 tff(13581,plain,(node20(s104)), inference(lemma,lemma(discharge,[]))).
% 2.37/2.37 tff(13582,assumption,(node20(s104)), introduced(assumption)).
% 2.37/2.37 tff(13583,assumption,(~always19(s104)), introduced(assumption)).
% 2.37/2.37 tff(13584,plain,
% 2.37/2.37 ($false),
% 2.37/2.37 inference(unit_resolution,[status(thm)],[13239, 8579, 13583, 13582])).
% 2.37/2.37 tff(13585,plain,((~node20(s104)) | always19(s104)), inference(lemma,lemma(discharge,[]))).
% 2.37/2.37 tff(13586,plain,
% 2.37/2.37 (always19(s104)),
% 2.37/2.37 inference(unit_resolution,[status(thm)],[13585, 13581])).
% 2.37/2.37 tff(13587,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s38) | (~trans(s104, s38)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s38) | (~trans(s104, s38)))),
% 2.37/2.37 inference(rewrite,[status(thm)],[])).
% 2.37/2.37 tff(13588,plain,
% 2.37/2.37 (((~trans(s104, s38)) | (~always19(s104)) | always19(s38)) <=> ((~always19(s104)) | always19(s38) | (~trans(s104, s38)))),
% 2.37/2.37 inference(rewrite,[status(thm)],[])).
% 2.37/2.37 tff(13589,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s38)) | (~always19(s104)) | always19(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s38) | (~trans(s104, s38))))),
% 2.37/2.37 inference(monotonicity,[status(thm)],[13588])).
% 2.37/2.37 tff(13590,plain,
% 2.37/2.37 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s38)) | (~always19(s104)) | always19(s38))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s38) | (~trans(s104, s38)))),
% 2.37/2.37 inference(transitivity,[status(thm)],[13589, 13587])).
% 2.37/2.37 tff(13591,plain,
% 2.37/2.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s38)) | (~always19(s104)) | always19(s38))),
% 2.37/2.37 inference(quant_inst,[status(thm)],[])).
% 2.37/2.37 tff(13592,plain,
% 2.37/2.37 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s38) | (~trans(s104, s38))),
% 2.37/2.38 inference(modus_ponens,[status(thm)],[13591, 13590])).
% 2.37/2.38 tff(13593,plain,
% 2.37/2.38 ($false),
% 2.37/2.38 inference(unit_resolution,[status(thm)],[13592, 11812, 8567, 13586, 3446])).
% 2.37/2.38 tff(13594,plain,(~trans(s104, s38)), inference(lemma,lemma(discharge,[]))).
% 2.37/2.38 tff(13595,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s97) | (~trans(s104, s97)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s97) | (~trans(s104, s97)))),
% 2.37/2.38 inference(rewrite,[status(thm)],[])).
% 2.37/2.38 tff(13596,plain,
% 2.37/2.38 (((~trans(s104, s97)) | (~always19(s104)) | always19(s97)) <=> ((~always19(s104)) | always19(s97) | (~trans(s104, s97)))),
% 2.37/2.38 inference(rewrite,[status(thm)],[])).
% 2.37/2.38 tff(13597,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s97)) | (~always19(s104)) | always19(s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s97) | (~trans(s104, s97))))),
% 2.37/2.38 inference(monotonicity,[status(thm)],[13596])).
% 2.37/2.38 tff(13598,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s97)) | (~always19(s104)) | always19(s97))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s97) | (~trans(s104, s97)))),
% 2.37/2.38 inference(transitivity,[status(thm)],[13597, 13595])).
% 2.37/2.38 tff(13599,plain,
% 2.37/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s97)) | (~always19(s104)) | always19(s97))),
% 2.37/2.38 inference(quant_inst,[status(thm)],[])).
% 2.37/2.38 tff(13600,plain,
% 2.37/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s97) | (~trans(s104, s97))),
% 2.37/2.38 inference(modus_ponens,[status(thm)],[13599, 13598])).
% 2.37/2.38 tff(13601,plain,
% 2.37/2.38 ($false),
% 2.37/2.38 inference(unit_resolution,[status(thm)],[13600, 11823, 8567, 13586, 8612])).
% 2.37/2.38 tff(13602,plain,(~trans(s104, s97)), inference(lemma,lemma(discharge,[]))).
% 2.37/2.38 tff(13603,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s78) | (~trans(s104, s78)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s78) | (~trans(s104, s78)))),
% 2.37/2.38 inference(rewrite,[status(thm)],[])).
% 2.37/2.38 tff(13604,plain,
% 2.37/2.38 (((~trans(s104, s78)) | (~always19(s104)) | always19(s78)) <=> ((~always19(s104)) | always19(s78) | (~trans(s104, s78)))),
% 2.37/2.38 inference(rewrite,[status(thm)],[])).
% 2.37/2.38 tff(13605,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s78)) | (~always19(s104)) | always19(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s78) | (~trans(s104, s78))))),
% 2.37/2.38 inference(monotonicity,[status(thm)],[13604])).
% 2.37/2.38 tff(13606,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s78)) | (~always19(s104)) | always19(s78))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s78) | (~trans(s104, s78)))),
% 2.37/2.38 inference(transitivity,[status(thm)],[13605, 13603])).
% 2.37/2.38 tff(13607,plain,
% 2.37/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s78)) | (~always19(s104)) | always19(s78))),
% 2.37/2.38 inference(quant_inst,[status(thm)],[])).
% 2.37/2.38 tff(13608,plain,
% 2.37/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s78) | (~trans(s104, s78))),
% 2.37/2.38 inference(modus_ponens,[status(thm)],[13607, 13606])).
% 2.37/2.38 tff(13609,plain,
% 2.37/2.38 ($false),
% 2.37/2.38 inference(unit_resolution,[status(thm)],[13608, 11801, 8567, 13586, 8772])).
% 2.37/2.38 tff(13610,plain,(~trans(s104, s78)), inference(lemma,lemma(discharge,[]))).
% 2.37/2.38 tff(13611,plain,
% 2.37/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s72) | (~trans(s104, s72)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s72) | (~trans(s104, s72)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13612,plain,
% 2.46/2.38 (((~trans(s104, s72)) | (~always19(s104)) | always19(s72)) <=> ((~always19(s104)) | always19(s72) | (~trans(s104, s72)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13613,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s72)) | (~always19(s104)) | always19(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s72) | (~trans(s104, s72))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13612])).
% 2.46/2.38 tff(13614,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s72)) | (~always19(s104)) | always19(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s72) | (~trans(s104, s72)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13613, 13611])).
% 2.46/2.38 tff(13615,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s72)) | (~always19(s104)) | always19(s72))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13616,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s72) | (~trans(s104, s72))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13615, 13614])).
% 2.46/2.38 tff(13617,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13616, 11834, 8567, 13586, 8819])).
% 2.46/2.38 tff(13618,plain,(~trans(s104, s72)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13619,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s35, s36)) | (~always19(s35)) | always19(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s35, s36)) | (~always19(s35)) | always19(s36))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13620,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s35, s36)) | (~always19(s35)) | always19(s36))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13621,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s35, s36)) | (~always19(s35)) | always19(s36)),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13620, 13619])).
% 2.46/2.38 tff(13622,plain,
% 2.46/2.38 ((~always19(s35)) | always19(s36)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13621, 8567, 3264])).
% 2.46/2.38 tff(13623,plain,
% 2.46/2.38 (~always19(s35)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13622, 9109])).
% 2.46/2.38 tff(13624,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s35) | (~trans(s104, s35)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s35) | (~trans(s104, s35)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13625,plain,
% 2.46/2.38 (((~trans(s104, s35)) | (~always19(s104)) | always19(s35)) <=> ((~always19(s104)) | always19(s35) | (~trans(s104, s35)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13626,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s35)) | (~always19(s104)) | always19(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s35) | (~trans(s104, s35))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13625])).
% 2.46/2.38 tff(13627,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s35)) | (~always19(s104)) | always19(s35))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s35) | (~trans(s104, s35)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13626, 13624])).
% 2.46/2.38 tff(13628,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s35)) | (~always19(s104)) | always19(s35))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13629,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s35) | (~trans(s104, s35))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13628, 13627])).
% 2.46/2.38 tff(13630,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13629, 11845, 8567, 13586, 13623])).
% 2.46/2.38 tff(13631,plain,(~trans(s104, s35)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13632,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s66) | (~trans(s104, s66)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s66) | (~trans(s104, s66)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13633,plain,
% 2.46/2.38 (((~trans(s104, s66)) | (~always19(s104)) | always19(s66)) <=> ((~always19(s104)) | always19(s66) | (~trans(s104, s66)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13634,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s66)) | (~always19(s104)) | always19(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s66) | (~trans(s104, s66))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13633])).
% 2.46/2.38 tff(13635,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s66)) | (~always19(s104)) | always19(s66))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s66) | (~trans(s104, s66)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13634, 13632])).
% 2.46/2.38 tff(13636,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s66)) | (~always19(s104)) | always19(s66))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13637,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s66) | (~trans(s104, s66))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13636, 13635])).
% 2.46/2.38 tff(13638,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13637, 11856, 8567, 13586, 8871])).
% 2.46/2.38 tff(13639,plain,(~trans(s104, s66)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13640,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s68) | (~trans(s104, s68)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s68) | (~trans(s104, s68)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13641,plain,
% 2.46/2.38 (((~trans(s104, s68)) | (~always19(s104)) | always19(s68)) <=> ((~always19(s104)) | always19(s68) | (~trans(s104, s68)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13642,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s68)) | (~always19(s104)) | always19(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s68) | (~trans(s104, s68))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13641])).
% 2.46/2.38 tff(13643,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s68)) | (~always19(s104)) | always19(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s68) | (~trans(s104, s68)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13642, 13640])).
% 2.46/2.38 tff(13644,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s68)) | (~always19(s104)) | always19(s68))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13645,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s68) | (~trans(s104, s68))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13644, 13643])).
% 2.46/2.38 tff(13646,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13645, 11867, 8567, 13586, 8852])).
% 2.46/2.38 tff(13647,plain,(~trans(s104, s68)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13648,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s10) | (~trans(s104, s10)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s10) | (~trans(s104, s10)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13649,plain,
% 2.46/2.38 (((~trans(s104, s10)) | (~always19(s104)) | always19(s10)) <=> ((~always19(s104)) | always19(s10) | (~trans(s104, s10)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13650,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s10)) | (~always19(s104)) | always19(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s10) | (~trans(s104, s10))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13649])).
% 2.46/2.38 tff(13651,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s10)) | (~always19(s104)) | always19(s10))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s10) | (~trans(s104, s10)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13650, 13648])).
% 2.46/2.38 tff(13652,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s10)) | (~always19(s104)) | always19(s10))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13653,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s10) | (~trans(s104, s10))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13652, 13651])).
% 2.46/2.38 tff(13654,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13653, 11978, 8567, 13586, 9326])).
% 2.46/2.38 tff(13655,plain,(~trans(s104, s10)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13656,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s23, s24)) | (~always19(s23)) | always19(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s23, s24)) | (~always19(s23)) | always19(s24))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13657,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s23, s24)) | (~always19(s23)) | always19(s24))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13658,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s23, s24)) | (~always19(s23)) | always19(s24)),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13657, 13656])).
% 2.46/2.38 tff(13659,plain,
% 2.46/2.38 ((~always19(s23)) | always19(s24)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13658, 8567, 2303])).
% 2.46/2.38 tff(13660,plain,
% 2.46/2.38 (~always19(s23)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13659, 9208])).
% 2.46/2.38 tff(13661,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s23) | (~trans(s104, s23)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s23) | (~trans(s104, s23)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13662,plain,
% 2.46/2.38 (((~trans(s104, s23)) | (~always19(s104)) | always19(s23)) <=> ((~always19(s104)) | always19(s23) | (~trans(s104, s23)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13663,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s23)) | (~always19(s104)) | always19(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s23) | (~trans(s104, s23))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13662])).
% 2.46/2.38 tff(13664,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s23)) | (~always19(s104)) | always19(s23))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s23) | (~trans(s104, s23)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13663, 13661])).
% 2.46/2.38 tff(13665,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s23)) | (~always19(s104)) | always19(s23))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13666,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s23) | (~trans(s104, s23))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13665, 13664])).
% 2.46/2.38 tff(13667,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13666, 11989, 8567, 13586, 13660])).
% 2.46/2.38 tff(13668,plain,(~trans(s104, s23)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13669,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s74) | (~trans(s104, s74)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s74) | (~trans(s104, s74)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13670,plain,
% 2.46/2.38 (((~trans(s104, s74)) | (~always19(s104)) | always19(s74)) <=> ((~always19(s104)) | always19(s74) | (~trans(s104, s74)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13671,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s74)) | (~always19(s104)) | always19(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s74) | (~trans(s104, s74))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13670])).
% 2.46/2.38 tff(13672,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s74)) | (~always19(s104)) | always19(s74))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s74) | (~trans(s104, s74)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13671, 13669])).
% 2.46/2.38 tff(13673,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s74)) | (~always19(s104)) | always19(s74))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13674,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s74) | (~trans(s104, s74))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13673, 13672])).
% 2.46/2.38 tff(13675,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13674, 12000, 8567, 13586, 8805])).
% 2.46/2.38 tff(13676,plain,(~trans(s104, s74)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13677,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s96) | (~trans(s104, s96)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s96) | (~trans(s104, s96)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13678,plain,
% 2.46/2.38 (((~trans(s104, s96)) | (~always19(s104)) | always19(s96)) <=> ((~always19(s104)) | always19(s96) | (~trans(s104, s96)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13679,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s96)) | (~always19(s104)) | always19(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s96) | (~trans(s104, s96))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13678])).
% 2.46/2.38 tff(13680,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s96)) | (~always19(s104)) | always19(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s96) | (~trans(s104, s96)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13679, 13677])).
% 2.46/2.38 tff(13681,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s96)) | (~always19(s104)) | always19(s96))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13682,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s96) | (~trans(s104, s96))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13681, 13680])).
% 2.46/2.38 tff(13683,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13682, 12011, 8567, 13586, 8621])).
% 2.46/2.38 tff(13684,plain,(~trans(s104, s96)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13685,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s16) | (~trans(s104, s16)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s16) | (~trans(s104, s16)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13686,plain,
% 2.46/2.38 (((~trans(s104, s16)) | (~always19(s104)) | always19(s16)) <=> ((~always19(s104)) | always19(s16) | (~trans(s104, s16)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13687,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s16)) | (~always19(s104)) | always19(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s16) | (~trans(s104, s16))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13686])).
% 2.46/2.38 tff(13688,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s16)) | (~always19(s104)) | always19(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s16) | (~trans(s104, s16)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13687, 13685])).
% 2.46/2.38 tff(13689,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s16)) | (~always19(s104)) | always19(s16))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13690,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s16) | (~trans(s104, s16))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13689, 13688])).
% 2.46/2.38 tff(13691,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13690, 12022, 8567, 13586, 9274])).
% 2.46/2.38 tff(13692,plain,(~trans(s104, s16)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13693,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s81) | (~trans(s104, s81)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s81) | (~trans(s104, s81)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13694,plain,
% 2.46/2.38 (((~trans(s104, s81)) | (~always19(s104)) | always19(s81)) <=> ((~always19(s104)) | always19(s81) | (~trans(s104, s81)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13695,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s81)) | (~always19(s104)) | always19(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s81) | (~trans(s104, s81))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13694])).
% 2.46/2.38 tff(13696,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s81)) | (~always19(s104)) | always19(s81))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s81) | (~trans(s104, s81)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13695, 13693])).
% 2.46/2.38 tff(13697,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s81)) | (~always19(s104)) | always19(s81))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13698,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s81) | (~trans(s104, s81))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13697, 13696])).
% 2.46/2.38 tff(13699,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13698, 12033, 8567, 13586, 8744])).
% 2.46/2.38 tff(13700,plain,(~trans(s104, s81)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13701,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s19, s20)) | (~always19(s19)) | always19(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s19, s20)) | (~always19(s19)) | always19(s20))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13702,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s19, s20)) | (~always19(s19)) | always19(s20))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13703,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s19, s20)) | (~always19(s19)) | always19(s20)),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13702, 13701])).
% 2.46/2.38 tff(13704,plain,
% 2.46/2.38 ((~always19(s19)) | always19(s20)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13703, 8567, 2008])).
% 2.46/2.38 tff(13705,plain,
% 2.46/2.38 (~always19(s19)),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13704, 9241])).
% 2.46/2.38 tff(13706,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s19) | (~trans(s104, s19)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s19) | (~trans(s104, s19)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13707,plain,
% 2.46/2.38 (((~trans(s104, s19)) | (~always19(s104)) | always19(s19)) <=> ((~always19(s104)) | always19(s19) | (~trans(s104, s19)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13708,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s19)) | (~always19(s104)) | always19(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s19) | (~trans(s104, s19))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13707])).
% 2.46/2.38 tff(13709,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s19)) | (~always19(s104)) | always19(s19))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s19) | (~trans(s104, s19)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13708, 13706])).
% 2.46/2.38 tff(13710,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s19)) | (~always19(s104)) | always19(s19))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13711,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s19) | (~trans(s104, s19))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13710, 13709])).
% 2.46/2.38 tff(13712,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13711, 12044, 8567, 13586, 13705])).
% 2.46/2.38 tff(13713,plain,(~trans(s104, s19)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13714,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s54) | (~trans(s104, s54)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s54) | (~trans(s104, s54)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13715,plain,
% 2.46/2.38 (((~trans(s104, s54)) | (~always19(s104)) | always19(s54)) <=> ((~always19(s104)) | always19(s54) | (~trans(s104, s54)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13716,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s54)) | (~always19(s104)) | always19(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s54) | (~trans(s104, s54))))),
% 2.46/2.38 inference(monotonicity,[status(thm)],[13715])).
% 2.46/2.38 tff(13717,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s54)) | (~always19(s104)) | always19(s54))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s54) | (~trans(s104, s54)))),
% 2.46/2.38 inference(transitivity,[status(thm)],[13716, 13714])).
% 2.46/2.38 tff(13718,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s54)) | (~always19(s104)) | always19(s54))),
% 2.46/2.38 inference(quant_inst,[status(thm)],[])).
% 2.46/2.38 tff(13719,plain,
% 2.46/2.38 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s54) | (~trans(s104, s54))),
% 2.46/2.38 inference(modus_ponens,[status(thm)],[13718, 13717])).
% 2.46/2.38 tff(13720,plain,
% 2.46/2.38 ($false),
% 2.46/2.38 inference(unit_resolution,[status(thm)],[13719, 12055, 8567, 13586, 8970])).
% 2.46/2.38 tff(13721,plain,(~trans(s104, s54)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.38 tff(13722,plain,
% 2.46/2.38 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s88) | (~trans(s104, s88)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s88) | (~trans(s104, s88)))),
% 2.46/2.38 inference(rewrite,[status(thm)],[])).
% 2.46/2.38 tff(13723,plain,
% 2.46/2.39 (((~trans(s104, s88)) | (~always19(s104)) | always19(s88)) <=> ((~always19(s104)) | always19(s88) | (~trans(s104, s88)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13724,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s88)) | (~always19(s104)) | always19(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s88) | (~trans(s104, s88))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13723])).
% 2.46/2.39 tff(13725,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s88)) | (~always19(s104)) | always19(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s88) | (~trans(s104, s88)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13724, 13722])).
% 2.46/2.39 tff(13726,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s88)) | (~always19(s104)) | always19(s88))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13727,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s88) | (~trans(s104, s88))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13726, 13725])).
% 2.46/2.39 tff(13728,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13727, 12066, 8567, 13586, 8687])).
% 2.46/2.39 tff(13729,plain,(~trans(s104, s88)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13730,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s39, s40)) | (~always19(s39)) | always19(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s39, s40)) | (~always19(s39)) | always19(s40))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13731,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s39, s40)) | (~always19(s39)) | always19(s40))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13732,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s39, s40)) | (~always19(s39)) | always19(s40)),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13731, 13730])).
% 2.46/2.39 tff(13733,plain,
% 2.46/2.39 ((~always19(s39)) | always19(s40)),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13732, 8567, 3574])).
% 2.46/2.39 tff(13734,plain,
% 2.46/2.39 (~always19(s39)),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13733, 9083])).
% 2.46/2.39 tff(13735,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s39) | (~trans(s104, s39)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s39) | (~trans(s104, s39)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13736,plain,
% 2.46/2.39 (((~trans(s104, s39)) | (~always19(s104)) | always19(s39)) <=> ((~always19(s104)) | always19(s39) | (~trans(s104, s39)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13737,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s39)) | (~always19(s104)) | always19(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s39) | (~trans(s104, s39))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13736])).
% 2.46/2.39 tff(13738,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s39)) | (~always19(s104)) | always19(s39))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s39) | (~trans(s104, s39)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13737, 13735])).
% 2.46/2.39 tff(13739,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s39)) | (~always19(s104)) | always19(s39))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13740,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s39) | (~trans(s104, s39))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13739, 13738])).
% 2.46/2.39 tff(13741,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13740, 12077, 8567, 13586, 13734])).
% 2.46/2.39 tff(13742,plain,(~trans(s104, s39)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13743,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s57) | (~trans(s104, s57)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s57) | (~trans(s104, s57)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13744,plain,
% 2.46/2.39 (((~trans(s104, s57)) | (~always19(s104)) | always19(s57)) <=> ((~always19(s104)) | always19(s57) | (~trans(s104, s57)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13745,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s57)) | (~always19(s104)) | always19(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s57) | (~trans(s104, s57))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13744])).
% 2.46/2.39 tff(13746,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s57)) | (~always19(s104)) | always19(s57))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s57) | (~trans(s104, s57)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13745, 13743])).
% 2.46/2.39 tff(13747,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s57)) | (~always19(s104)) | always19(s57))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13748,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s57) | (~trans(s104, s57))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13747, 13746])).
% 2.46/2.39 tff(13749,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13748, 12088, 8567, 13586, 8942])).
% 2.46/2.39 tff(13750,plain,(~trans(s104, s57)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13751,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s33) | (~trans(s104, s33)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s33) | (~trans(s104, s33)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13752,plain,
% 2.46/2.39 (((~trans(s104, s33)) | (~always19(s104)) | always19(s33)) <=> ((~always19(s104)) | always19(s33) | (~trans(s104, s33)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13753,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s33)) | (~always19(s104)) | always19(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s33) | (~trans(s104, s33))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13752])).
% 2.46/2.39 tff(13754,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s33)) | (~always19(s104)) | always19(s33))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s33) | (~trans(s104, s33)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13753, 13751])).
% 2.46/2.39 tff(13755,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s33)) | (~always19(s104)) | always19(s33))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13756,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s33) | (~trans(s104, s33))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13755, 13754])).
% 2.46/2.39 tff(13757,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13756, 12099, 8567, 13586, 9133])).
% 2.46/2.39 tff(13758,plain,(~trans(s104, s33)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13759,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s15, s16)) | (~always19(s15)) | always19(s16))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s15, s16)) | (~always19(s15)) | always19(s16))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13760,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s15, s16)) | (~always19(s15)) | always19(s16))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13761,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s15, s16)) | (~always19(s15)) | always19(s16)),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13760, 13759])).
% 2.46/2.39 tff(13762,plain,
% 2.46/2.39 ((~always19(s15)) | always19(s16)),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13761, 8567, 1675])).
% 2.46/2.39 tff(13763,plain,
% 2.46/2.39 (~always19(s15)),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13762, 9274])).
% 2.46/2.39 tff(13764,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s15) | (~trans(s104, s15)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s15) | (~trans(s104, s15)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13765,plain,
% 2.46/2.39 (((~trans(s104, s15)) | (~always19(s104)) | always19(s15)) <=> ((~always19(s104)) | always19(s15) | (~trans(s104, s15)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13766,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s15)) | (~always19(s104)) | always19(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s15) | (~trans(s104, s15))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13765])).
% 2.46/2.39 tff(13767,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s15)) | (~always19(s104)) | always19(s15))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s15) | (~trans(s104, s15)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13766, 13764])).
% 2.46/2.39 tff(13768,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s15)) | (~always19(s104)) | always19(s15))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13769,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s15) | (~trans(s104, s15))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13768, 13767])).
% 2.46/2.39 tff(13770,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13769, 12110, 8567, 13586, 13763])).
% 2.46/2.39 tff(13771,plain,(~trans(s104, s15)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13772,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s9) | (~trans(s104, s9)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s9) | (~trans(s104, s9)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13773,plain,
% 2.46/2.39 (((~trans(s104, s9)) | (~always19(s104)) | always19(s9)) <=> ((~always19(s104)) | always19(s9) | (~trans(s104, s9)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13774,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s9)) | (~always19(s104)) | always19(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s9) | (~trans(s104, s9))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13773])).
% 2.46/2.39 tff(13775,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s9)) | (~always19(s104)) | always19(s9))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s9) | (~trans(s104, s9)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13774, 13772])).
% 2.46/2.39 tff(13776,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s9)) | (~always19(s104)) | always19(s9))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13777,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s9) | (~trans(s104, s9))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13776, 13775])).
% 2.46/2.39 tff(13778,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13777, 12131, 8567, 13586, 9331])).
% 2.46/2.39 tff(13779,plain,(~trans(s104, s9)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13780,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s62) | (~trans(s104, s62)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s62) | (~trans(s104, s62)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13781,plain,
% 2.46/2.39 (((~trans(s104, s62)) | (~always19(s104)) | always19(s62)) <=> ((~always19(s104)) | always19(s62) | (~trans(s104, s62)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13782,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s62)) | (~always19(s104)) | always19(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s62) | (~trans(s104, s62))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13781])).
% 2.46/2.39 tff(13783,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s62)) | (~always19(s104)) | always19(s62))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s62) | (~trans(s104, s62)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13782, 13780])).
% 2.46/2.39 tff(13784,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s62)) | (~always19(s104)) | always19(s62))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13785,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s62) | (~trans(s104, s62))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13784, 13783])).
% 2.46/2.39 tff(13786,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13785, 12142, 8567, 13586, 8904])).
% 2.46/2.39 tff(13787,plain,(~trans(s104, s62)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13788,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s70) | (~trans(s104, s70)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s70) | (~trans(s104, s70)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13789,plain,
% 2.46/2.39 (((~trans(s104, s70)) | (~always19(s104)) | always19(s70)) <=> ((~always19(s104)) | always19(s70) | (~trans(s104, s70)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13790,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s70)) | (~always19(s104)) | always19(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s70) | (~trans(s104, s70))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13789])).
% 2.46/2.39 tff(13791,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s70)) | (~always19(s104)) | always19(s70))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s70) | (~trans(s104, s70)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13790, 13788])).
% 2.46/2.39 tff(13792,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s70)) | (~always19(s104)) | always19(s70))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13793,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s70) | (~trans(s104, s70))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13792, 13791])).
% 2.46/2.39 tff(13794,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13793, 12153, 8567, 13586, 8838])).
% 2.46/2.39 tff(13795,plain,(~trans(s104, s70)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13796,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s48) | (~trans(s104, s48)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s48) | (~trans(s104, s48)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13797,plain,
% 2.46/2.39 (((~trans(s104, s48)) | (~always19(s104)) | always19(s48)) <=> ((~always19(s104)) | always19(s48) | (~trans(s104, s48)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13798,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s48)) | (~always19(s104)) | always19(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s48) | (~trans(s104, s48))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13797])).
% 2.46/2.39 tff(13799,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s48)) | (~always19(s104)) | always19(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s48) | (~trans(s104, s48)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13798, 13796])).
% 2.46/2.39 tff(13800,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s48)) | (~always19(s104)) | always19(s48))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13801,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s48) | (~trans(s104, s48))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13800, 13799])).
% 2.46/2.39 tff(13802,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13801, 12164, 8567, 13586, 9017])).
% 2.46/2.39 tff(13803,plain,(~trans(s104, s48)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13804,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s13) | (~trans(s104, s13)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s13) | (~trans(s104, s13)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13805,plain,
% 2.46/2.39 (((~trans(s104, s13)) | (~always19(s104)) | always19(s13)) <=> ((~always19(s104)) | always19(s13) | (~trans(s104, s13)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13806,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s13)) | (~always19(s104)) | always19(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s13) | (~trans(s104, s13))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13805])).
% 2.46/2.39 tff(13807,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s13)) | (~always19(s104)) | always19(s13))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s13) | (~trans(s104, s13)))),
% 2.46/2.39 inference(transitivity,[status(thm)],[13806, 13804])).
% 2.46/2.39 tff(13808,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s13)) | (~always19(s104)) | always19(s13))),
% 2.46/2.39 inference(quant_inst,[status(thm)],[])).
% 2.46/2.39 tff(13809,plain,
% 2.46/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s13) | (~trans(s104, s13))),
% 2.46/2.39 inference(modus_ponens,[status(thm)],[13808, 13807])).
% 2.46/2.39 tff(13810,plain,
% 2.46/2.39 ($false),
% 2.46/2.39 inference(unit_resolution,[status(thm)],[13809, 12175, 8567, 13586, 9298])).
% 2.46/2.39 tff(13811,plain,(~trans(s104, s13)), inference(lemma,lemma(discharge,[]))).
% 2.46/2.39 tff(13812,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s37) | (~trans(s104, s37)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s37) | (~trans(s104, s37)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13813,plain,
% 2.46/2.39 (((~trans(s104, s37)) | (~always19(s104)) | always19(s37)) <=> ((~always19(s104)) | always19(s37) | (~trans(s104, s37)))),
% 2.46/2.39 inference(rewrite,[status(thm)],[])).
% 2.46/2.39 tff(13814,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s37)) | (~always19(s104)) | always19(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s37) | (~trans(s104, s37))))),
% 2.46/2.39 inference(monotonicity,[status(thm)],[13813])).
% 2.46/2.39 tff(13815,plain,
% 2.46/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s37)) | (~always19(s104)) | always19(s37))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s37) | (~trans(s104, s37)))),
% 2.48/2.39 inference(transitivity,[status(thm)],[13814, 13812])).
% 2.48/2.39 tff(13816,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s37)) | (~always19(s104)) | always19(s37))),
% 2.48/2.39 inference(quant_inst,[status(thm)],[])).
% 2.48/2.39 tff(13817,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s37) | (~trans(s104, s37))),
% 2.48/2.39 inference(modus_ponens,[status(thm)],[13816, 13815])).
% 2.48/2.39 tff(13818,plain,
% 2.48/2.39 ($false),
% 2.48/2.39 inference(unit_resolution,[status(thm)],[13817, 12186, 8567, 13586, 9100])).
% 2.48/2.39 tff(13819,plain,(~trans(s104, s37)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.39 tff(13820,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s102) | (~trans(s104, s102)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s102) | (~trans(s104, s102)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13821,plain,
% 2.48/2.39 (((~trans(s104, s102)) | (~always19(s104)) | always19(s102)) <=> ((~always19(s104)) | always19(s102) | (~trans(s104, s102)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13822,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s102)) | (~always19(s104)) | always19(s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s102) | (~trans(s104, s102))))),
% 2.48/2.39 inference(monotonicity,[status(thm)],[13821])).
% 2.48/2.39 tff(13823,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s102)) | (~always19(s104)) | always19(s102))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s102) | (~trans(s104, s102)))),
% 2.48/2.39 inference(transitivity,[status(thm)],[13822, 13820])).
% 2.48/2.39 tff(13824,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s102)) | (~always19(s104)) | always19(s102))),
% 2.48/2.39 inference(quant_inst,[status(thm)],[])).
% 2.48/2.39 tff(13825,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s102) | (~trans(s104, s102))),
% 2.48/2.39 inference(modus_ponens,[status(thm)],[13824, 13823])).
% 2.48/2.39 tff(13826,plain,
% 2.48/2.39 ($false),
% 2.48/2.39 inference(unit_resolution,[status(thm)],[13825, 12197, 8567, 13586, 8557])).
% 2.48/2.39 tff(13827,plain,(~trans(s104, s102)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.39 tff(13828,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s2) | (~trans(s104, s2)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s2) | (~trans(s104, s2)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13829,plain,
% 2.48/2.39 (((~trans(s104, s2)) | (~always19(s104)) | always19(s2)) <=> ((~always19(s104)) | always19(s2) | (~trans(s104, s2)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13830,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s2)) | (~always19(s104)) | always19(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s2) | (~trans(s104, s2))))),
% 2.48/2.39 inference(monotonicity,[status(thm)],[13829])).
% 2.48/2.39 tff(13831,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s2)) | (~always19(s104)) | always19(s2))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s2) | (~trans(s104, s2)))),
% 2.48/2.39 inference(transitivity,[status(thm)],[13830, 13828])).
% 2.48/2.39 tff(13832,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s2)) | (~always19(s104)) | always19(s2))),
% 2.48/2.39 inference(quant_inst,[status(thm)],[])).
% 2.48/2.39 tff(13833,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s2) | (~trans(s104, s2))),
% 2.48/2.39 inference(modus_ponens,[status(thm)],[13832, 13831])).
% 2.48/2.39 tff(13834,plain,
% 2.48/2.39 ($false),
% 2.48/2.39 inference(unit_resolution,[status(thm)],[13833, 12278, 8567, 13586, 9392])).
% 2.48/2.39 tff(13835,plain,(~trans(s104, s2)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.39 tff(13836,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s52) | (~trans(s104, s52)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s52) | (~trans(s104, s52)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13837,plain,
% 2.48/2.39 (((~trans(s104, s52)) | (~always19(s104)) | always19(s52)) <=> ((~always19(s104)) | always19(s52) | (~trans(s104, s52)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13838,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s52)) | (~always19(s104)) | always19(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s52) | (~trans(s104, s52))))),
% 2.48/2.39 inference(monotonicity,[status(thm)],[13837])).
% 2.48/2.39 tff(13839,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s52)) | (~always19(s104)) | always19(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s52) | (~trans(s104, s52)))),
% 2.48/2.39 inference(transitivity,[status(thm)],[13838, 13836])).
% 2.48/2.39 tff(13840,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s52)) | (~always19(s104)) | always19(s52))),
% 2.48/2.39 inference(quant_inst,[status(thm)],[])).
% 2.48/2.39 tff(13841,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s52) | (~trans(s104, s52))),
% 2.48/2.39 inference(modus_ponens,[status(thm)],[13840, 13839])).
% 2.48/2.39 tff(13842,plain,
% 2.48/2.39 ($false),
% 2.48/2.39 inference(unit_resolution,[status(thm)],[13841, 12289, 8567, 13586, 8984])).
% 2.48/2.39 tff(13843,plain,(~trans(s104, s52)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.39 tff(13844,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s29) | (~trans(s104, s29)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s29) | (~trans(s104, s29)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13845,plain,
% 2.48/2.39 (((~trans(s104, s29)) | (~always19(s104)) | always19(s29)) <=> ((~always19(s104)) | always19(s29) | (~trans(s104, s29)))),
% 2.48/2.39 inference(rewrite,[status(thm)],[])).
% 2.48/2.39 tff(13846,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s29)) | (~always19(s104)) | always19(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s29) | (~trans(s104, s29))))),
% 2.48/2.39 inference(monotonicity,[status(thm)],[13845])).
% 2.48/2.39 tff(13847,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s29)) | (~always19(s104)) | always19(s29))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s29) | (~trans(s104, s29)))),
% 2.48/2.39 inference(transitivity,[status(thm)],[13846, 13844])).
% 2.48/2.39 tff(13848,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s29)) | (~always19(s104)) | always19(s29))),
% 2.48/2.39 inference(quant_inst,[status(thm)],[])).
% 2.48/2.39 tff(13849,plain,
% 2.48/2.39 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s29) | (~trans(s104, s29))),
% 2.48/2.39 inference(modus_ponens,[status(thm)],[13848, 13847])).
% 2.48/2.39 tff(13850,plain,
% 2.48/2.39 ($false),
% 2.48/2.39 inference(unit_resolution,[status(thm)],[13849, 12300, 8567, 13586, 9166])).
% 2.48/2.39 tff(13851,plain,(~trans(s104, s29)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.39 tff(13852,plain,
% 2.48/2.39 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s31, s32)) | (~always19(s31)) | always19(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s31, s32)) | (~always19(s31)) | always19(s32))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13853,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s31, s32)) | (~always19(s31)) | always19(s32))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13854,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s31, s32)) | (~always19(s31)) | always19(s32)),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13853, 13852])).
% 2.48/2.40 tff(13855,plain,
% 2.48/2.40 ((~always19(s31)) | always19(s32)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13854, 8567, 2931])).
% 2.48/2.40 tff(13856,plain,
% 2.48/2.40 (~always19(s31)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13855, 9142])).
% 2.48/2.40 tff(13857,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s31) | (~trans(s104, s31)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s31) | (~trans(s104, s31)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13858,plain,
% 2.48/2.40 (((~trans(s104, s31)) | (~always19(s104)) | always19(s31)) <=> ((~always19(s104)) | always19(s31) | (~trans(s104, s31)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13859,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s31)) | (~always19(s104)) | always19(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s31) | (~trans(s104, s31))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13858])).
% 2.48/2.40 tff(13860,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s31)) | (~always19(s104)) | always19(s31))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s31) | (~trans(s104, s31)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13859, 13857])).
% 2.48/2.40 tff(13861,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s31)) | (~always19(s104)) | always19(s31))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13862,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s31) | (~trans(s104, s31))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13861, 13860])).
% 2.48/2.40 tff(13863,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13862, 12311, 8567, 13586, 13856])).
% 2.48/2.40 tff(13864,plain,(~trans(s104, s31)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13865,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s55, s56)) | (~always19(s55)) | always19(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s55, s56)) | (~always19(s55)) | always19(s56))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13866,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s55, s56)) | (~always19(s55)) | always19(s56))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13867,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s55, s56)) | (~always19(s55)) | always19(s56)),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13866, 13865])).
% 2.48/2.40 tff(13868,plain,
% 2.48/2.40 ((~always19(s55)) | always19(s56)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13867, 8567, 4830])).
% 2.48/2.40 tff(13869,plain,
% 2.48/2.40 (~always19(s55)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13868, 8951])).
% 2.48/2.40 tff(13870,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s55) | (~trans(s104, s55)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s55) | (~trans(s104, s55)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13871,plain,
% 2.48/2.40 (((~trans(s104, s55)) | (~always19(s104)) | always19(s55)) <=> ((~always19(s104)) | always19(s55) | (~trans(s104, s55)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13872,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s55)) | (~always19(s104)) | always19(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s55) | (~trans(s104, s55))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13871])).
% 2.48/2.40 tff(13873,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s55)) | (~always19(s104)) | always19(s55))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s55) | (~trans(s104, s55)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13872, 13870])).
% 2.48/2.40 tff(13874,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s55)) | (~always19(s104)) | always19(s55))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13875,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s55) | (~trans(s104, s55))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13874, 13873])).
% 2.48/2.40 tff(13876,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13875, 12322, 8567, 13586, 13869])).
% 2.48/2.40 tff(13877,plain,(~trans(s104, s55)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13878,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s7, s8)) | (~always19(s7)) | always19(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s7, s8)) | (~always19(s7)) | always19(s8))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13879,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s7, s8)) | (~always19(s7)) | always19(s8))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13880,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s7, s8)) | (~always19(s7)) | always19(s8)),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13879, 13878])).
% 2.48/2.40 tff(13881,plain,
% 2.48/2.40 ((~always19(s7)) | always19(s8)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13880, 8567, 1047])).
% 2.48/2.40 tff(13882,plain,
% 2.48/2.40 (~always19(s7)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13881, 9340])).
% 2.48/2.40 tff(13883,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s7) | (~trans(s104, s7)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s7) | (~trans(s104, s7)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13884,plain,
% 2.48/2.40 (((~trans(s104, s7)) | (~always19(s104)) | always19(s7)) <=> ((~always19(s104)) | always19(s7) | (~trans(s104, s7)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13885,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s7)) | (~always19(s104)) | always19(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s7) | (~trans(s104, s7))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13884])).
% 2.48/2.40 tff(13886,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s7)) | (~always19(s104)) | always19(s7))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s7) | (~trans(s104, s7)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13885, 13883])).
% 2.48/2.40 tff(13887,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s7)) | (~always19(s104)) | always19(s7))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13888,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s7) | (~trans(s104, s7))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13887, 13886])).
% 2.48/2.40 tff(13889,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13888, 12333, 8567, 13586, 13882])).
% 2.48/2.40 tff(13890,plain,(~trans(s104, s7)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13891,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s64) | (~trans(s104, s64)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s64) | (~trans(s104, s64)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13892,plain,
% 2.48/2.40 (((~trans(s104, s64)) | (~always19(s104)) | always19(s64)) <=> ((~always19(s104)) | always19(s64) | (~trans(s104, s64)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13893,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s64)) | (~always19(s104)) | always19(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s64) | (~trans(s104, s64))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13892])).
% 2.48/2.40 tff(13894,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s64)) | (~always19(s104)) | always19(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s64) | (~trans(s104, s64)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13893, 13891])).
% 2.48/2.40 tff(13895,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s64)) | (~always19(s104)) | always19(s64))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13896,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s64) | (~trans(s104, s64))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13895, 13894])).
% 2.48/2.40 tff(13897,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13896, 12344, 8567, 13586, 8885])).
% 2.48/2.40 tff(13898,plain,(~trans(s104, s64)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13899,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s1) | (~trans(s104, s1)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s1) | (~trans(s104, s1)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13900,plain,
% 2.48/2.40 (((~trans(s104, s1)) | (~always19(s104)) | always19(s1)) <=> ((~always19(s104)) | always19(s1) | (~trans(s104, s1)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13901,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s1)) | (~always19(s104)) | always19(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s1) | (~trans(s104, s1))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13900])).
% 2.48/2.40 tff(13902,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s1)) | (~always19(s104)) | always19(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s1) | (~trans(s104, s1)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13901, 13899])).
% 2.48/2.40 tff(13903,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s1)) | (~always19(s104)) | always19(s1))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13904,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s1) | (~trans(s104, s1))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13903, 13902])).
% 2.48/2.40 tff(13905,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13904, 12365, 8567, 13586, 9401])).
% 2.48/2.40 tff(13906,plain,(~trans(s104, s1)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13907,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s99, s100)) | (~always19(s99)) | always19(s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s99, s100)) | (~always19(s99)) | always19(s100))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13908,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s99, s100)) | (~always19(s99)) | always19(s100))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13909,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s99, s100)) | (~always19(s99)) | always19(s100)),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13908, 13907])).
% 2.48/2.40 tff(13910,plain,
% 2.48/2.40 ((~always19(s99)) | always19(s100)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13909, 8567, 8303])).
% 2.48/2.40 tff(13911,plain,
% 2.48/2.40 (~always19(s99)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13910, 8588])).
% 2.48/2.40 tff(13912,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s99) | (~trans(s104, s99)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s99) | (~trans(s104, s99)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13913,plain,
% 2.48/2.40 (((~trans(s104, s99)) | (~always19(s104)) | always19(s99)) <=> ((~always19(s104)) | always19(s99) | (~trans(s104, s99)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13914,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s99)) | (~always19(s104)) | always19(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s99) | (~trans(s104, s99))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13913])).
% 2.48/2.40 tff(13915,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s99)) | (~always19(s104)) | always19(s99))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s99) | (~trans(s104, s99)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13914, 13912])).
% 2.48/2.40 tff(13916,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s99)) | (~always19(s104)) | always19(s99))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13917,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s99) | (~trans(s104, s99))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13916, 13915])).
% 2.48/2.40 tff(13918,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13917, 12376, 8567, 13586, 13911])).
% 2.48/2.40 tff(13919,plain,(~trans(s104, s99)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13920,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s63, s64)) | (~always19(s63)) | always19(s64))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s63, s64)) | (~always19(s63)) | always19(s64))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13921,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s63, s64)) | (~always19(s63)) | always19(s64))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13922,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s63, s64)) | (~always19(s63)) | always19(s64)),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13921, 13920])).
% 2.48/2.40 tff(13923,plain,
% 2.48/2.40 ((~always19(s63)) | always19(s64)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13922, 8567, 5458])).
% 2.48/2.40 tff(13924,plain,
% 2.48/2.40 (~always19(s63)),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13923, 8885])).
% 2.48/2.40 tff(13925,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s63) | (~trans(s104, s63)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s63) | (~trans(s104, s63)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13926,plain,
% 2.48/2.40 (((~trans(s104, s63)) | (~always19(s104)) | always19(s63)) <=> ((~always19(s104)) | always19(s63) | (~trans(s104, s63)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13927,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s63)) | (~always19(s104)) | always19(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s63) | (~trans(s104, s63))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13926])).
% 2.48/2.40 tff(13928,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s63)) | (~always19(s104)) | always19(s63))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s63) | (~trans(s104, s63)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13927, 13925])).
% 2.48/2.40 tff(13929,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s63)) | (~always19(s104)) | always19(s63))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13930,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s63) | (~trans(s104, s63))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13929, 13928])).
% 2.48/2.40 tff(13931,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13930, 12387, 8567, 13586, 13924])).
% 2.48/2.40 tff(13932,plain,(~trans(s104, s63)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13933,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s25) | (~trans(s104, s25)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s25) | (~trans(s104, s25)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13934,plain,
% 2.48/2.40 (((~trans(s104, s25)) | (~always19(s104)) | always19(s25)) <=> ((~always19(s104)) | always19(s25) | (~trans(s104, s25)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13935,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s25)) | (~always19(s104)) | always19(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s25) | (~trans(s104, s25))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13934])).
% 2.48/2.40 tff(13936,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s25)) | (~always19(s104)) | always19(s25))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s25) | (~trans(s104, s25)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13935, 13933])).
% 2.48/2.40 tff(13937,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s25)) | (~always19(s104)) | always19(s25))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13938,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s25) | (~trans(s104, s25))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13937, 13936])).
% 2.48/2.40 tff(13939,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13938, 12398, 8567, 13586, 9199])).
% 2.48/2.40 tff(13940,plain,(~trans(s104, s25)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13941,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s73) | (~trans(s104, s73)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s73) | (~trans(s104, s73)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13942,plain,
% 2.48/2.40 (((~trans(s104, s73)) | (~always19(s104)) | always19(s73)) <=> ((~always19(s104)) | always19(s73) | (~trans(s104, s73)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13943,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s73)) | (~always19(s104)) | always19(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s73) | (~trans(s104, s73))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13942])).
% 2.48/2.40 tff(13944,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s73)) | (~always19(s104)) | always19(s73))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s73) | (~trans(s104, s73)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13943, 13941])).
% 2.48/2.40 tff(13945,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s73)) | (~always19(s104)) | always19(s73))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13946,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s73) | (~trans(s104, s73))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13945, 13944])).
% 2.48/2.40 tff(13947,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13946, 12409, 8567, 13586, 8810])).
% 2.48/2.40 tff(13948,plain,(~trans(s104, s73)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13949,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s12) | (~trans(s104, s12)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s12) | (~trans(s104, s12)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13950,plain,
% 2.48/2.40 (((~trans(s104, s12)) | (~always19(s104)) | always19(s12)) <=> ((~always19(s104)) | always19(s12) | (~trans(s104, s12)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13951,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s12)) | (~always19(s104)) | always19(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s12) | (~trans(s104, s12))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13950])).
% 2.48/2.40 tff(13952,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s12)) | (~always19(s104)) | always19(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s12) | (~trans(s104, s12)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13951, 13949])).
% 2.48/2.40 tff(13953,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s12)) | (~always19(s104)) | always19(s12))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13954,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s12) | (~trans(s104, s12))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13953, 13952])).
% 2.48/2.40 tff(13955,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13954, 12420, 8567, 13586, 9307])).
% 2.48/2.40 tff(13956,plain,(~trans(s104, s12)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13957,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s21) | (~trans(s104, s21)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s21) | (~trans(s104, s21)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13958,plain,
% 2.48/2.40 (((~trans(s104, s21)) | (~always19(s104)) | always19(s21)) <=> ((~always19(s104)) | always19(s21) | (~trans(s104, s21)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13959,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s21)) | (~always19(s104)) | always19(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s21) | (~trans(s104, s21))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13958])).
% 2.48/2.40 tff(13960,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s21)) | (~always19(s104)) | always19(s21))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s21) | (~trans(s104, s21)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13959, 13957])).
% 2.48/2.40 tff(13961,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s21)) | (~always19(s104)) | always19(s21))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13962,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s21) | (~trans(s104, s21))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13961, 13960])).
% 2.48/2.40 tff(13963,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13962, 12431, 8567, 13586, 9232])).
% 2.48/2.40 tff(13964,plain,(~trans(s104, s21)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13965,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s93) | (~trans(s104, s93)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s93) | (~trans(s104, s93)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13966,plain,
% 2.48/2.40 (((~trans(s104, s93)) | (~always19(s104)) | always19(s93)) <=> ((~always19(s104)) | always19(s93) | (~trans(s104, s93)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13967,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s93)) | (~always19(s104)) | always19(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s93) | (~trans(s104, s93))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13966])).
% 2.48/2.40 tff(13968,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s93)) | (~always19(s104)) | always19(s93))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s93) | (~trans(s104, s93)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13967, 13965])).
% 2.48/2.40 tff(13969,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s93)) | (~always19(s104)) | always19(s93))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13970,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s93) | (~trans(s104, s93))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13969, 13968])).
% 2.48/2.40 tff(13971,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13970, 12442, 8567, 13586, 8645])).
% 2.48/2.40 tff(13972,plain,(~trans(s104, s93)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13973,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s80) | (~trans(s104, s80)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s80) | (~trans(s104, s80)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13974,plain,
% 2.48/2.40 (((~trans(s104, s80)) | (~always19(s104)) | always19(s80)) <=> ((~always19(s104)) | always19(s80) | (~trans(s104, s80)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13975,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s80)) | (~always19(s104)) | always19(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s80) | (~trans(s104, s80))))),
% 2.48/2.40 inference(monotonicity,[status(thm)],[13974])).
% 2.48/2.40 tff(13976,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s80)) | (~always19(s104)) | always19(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s80) | (~trans(s104, s80)))),
% 2.48/2.40 inference(transitivity,[status(thm)],[13975, 13973])).
% 2.48/2.40 tff(13977,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s80)) | (~always19(s104)) | always19(s80))),
% 2.48/2.40 inference(quant_inst,[status(thm)],[])).
% 2.48/2.40 tff(13978,plain,
% 2.48/2.40 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s80) | (~trans(s104, s80))),
% 2.48/2.40 inference(modus_ponens,[status(thm)],[13977, 13976])).
% 2.48/2.40 tff(13979,plain,
% 2.48/2.40 ($false),
% 2.48/2.40 inference(unit_resolution,[status(thm)],[13978, 12453, 8567, 13586, 8753])).
% 2.48/2.40 tff(13980,plain,(~trans(s104, s80)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.40 tff(13981,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s28) | (~trans(s104, s28)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s28) | (~trans(s104, s28)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13982,plain,
% 2.48/2.40 (((~trans(s104, s28)) | (~always19(s104)) | always19(s28)) <=> ((~always19(s104)) | always19(s28) | (~trans(s104, s28)))),
% 2.48/2.40 inference(rewrite,[status(thm)],[])).
% 2.48/2.40 tff(13983,plain,
% 2.48/2.40 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s28)) | (~always19(s104)) | always19(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s28) | (~trans(s104, s28))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[13982])).
% 2.48/2.41 tff(13984,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s28)) | (~always19(s104)) | always19(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s28) | (~trans(s104, s28)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[13983, 13981])).
% 2.48/2.41 tff(13985,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s28)) | (~always19(s104)) | always19(s28))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(13986,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s28) | (~trans(s104, s28))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[13985, 13984])).
% 2.48/2.41 tff(13987,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[13986, 12464, 8567, 13586, 9175])).
% 2.48/2.41 tff(13988,plain,(~trans(s104, s28)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(13989,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s56) | (~trans(s104, s56)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s56) | (~trans(s104, s56)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(13990,plain,
% 2.48/2.41 (((~trans(s104, s56)) | (~always19(s104)) | always19(s56)) <=> ((~always19(s104)) | always19(s56) | (~trans(s104, s56)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(13991,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s56)) | (~always19(s104)) | always19(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s56) | (~trans(s104, s56))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[13990])).
% 2.48/2.41 tff(13992,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s56)) | (~always19(s104)) | always19(s56))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s56) | (~trans(s104, s56)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[13991, 13989])).
% 2.48/2.41 tff(13993,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s56)) | (~always19(s104)) | always19(s56))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(13994,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s56) | (~trans(s104, s56))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[13993, 13992])).
% 2.48/2.41 tff(13995,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[13994, 12475, 8567, 13586, 8951])).
% 2.48/2.41 tff(13996,plain,(~trans(s104, s56)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(13997,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s27, s28)) | (~always19(s27)) | always19(s28))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s27, s28)) | (~always19(s27)) | always19(s28))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(13998,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s27, s28)) | (~always19(s27)) | always19(s28))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(13999,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s27, s28)) | (~always19(s27)) | always19(s28)),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[13998, 13997])).
% 2.48/2.41 tff(14000,plain,
% 2.48/2.41 ((~always19(s27)) | always19(s28)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[13999, 8567, 2636])).
% 2.48/2.41 tff(14001,plain,
% 2.48/2.41 (~always19(s27)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14000, 9175])).
% 2.48/2.41 tff(14002,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s27) | (~trans(s104, s27)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s27) | (~trans(s104, s27)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14003,plain,
% 2.48/2.41 (((~trans(s104, s27)) | (~always19(s104)) | always19(s27)) <=> ((~always19(s104)) | always19(s27) | (~trans(s104, s27)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14004,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s27)) | (~always19(s104)) | always19(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s27) | (~trans(s104, s27))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14003])).
% 2.48/2.41 tff(14005,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s27)) | (~always19(s104)) | always19(s27))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s27) | (~trans(s104, s27)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14004, 14002])).
% 2.48/2.41 tff(14006,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s27)) | (~always19(s104)) | always19(s27))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14007,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s27) | (~trans(s104, s27))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14006, 14005])).
% 2.48/2.41 tff(14008,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14007, 12486, 8567, 13586, 14001])).
% 2.48/2.41 tff(14009,plain,(~trans(s104, s27)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(14010,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s75, s76)) | (~always19(s75)) | always19(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s75, s76)) | (~always19(s75)) | always19(s76))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14011,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s75, s76)) | (~always19(s75)) | always19(s76))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14012,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s75, s76)) | (~always19(s75)) | always19(s76)),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14011, 14010])).
% 2.48/2.41 tff(14013,plain,
% 2.48/2.41 ((~always19(s75)) | always19(s76)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14012, 8567, 6419])).
% 2.48/2.41 tff(14014,plain,
% 2.48/2.41 (~always19(s75)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14013, 8786])).
% 2.48/2.41 tff(14015,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s75) | (~trans(s104, s75)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s75) | (~trans(s104, s75)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14016,plain,
% 2.48/2.41 (((~trans(s104, s75)) | (~always19(s104)) | always19(s75)) <=> ((~always19(s104)) | always19(s75) | (~trans(s104, s75)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14017,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s75)) | (~always19(s104)) | always19(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s75) | (~trans(s104, s75))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14016])).
% 2.48/2.41 tff(14018,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s75)) | (~always19(s104)) | always19(s75))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s75) | (~trans(s104, s75)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14017, 14015])).
% 2.48/2.41 tff(14019,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s75)) | (~always19(s104)) | always19(s75))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14020,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s75) | (~trans(s104, s75))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14019, 14018])).
% 2.48/2.41 tff(14021,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14020, 12497, 8567, 13586, 14014])).
% 2.48/2.41 tff(14022,plain,(~trans(s104, s75)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(14023,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s76) | (~trans(s104, s76)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s76) | (~trans(s104, s76)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14024,plain,
% 2.48/2.41 (((~trans(s104, s76)) | (~always19(s104)) | always19(s76)) <=> ((~always19(s104)) | always19(s76) | (~trans(s104, s76)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14025,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s76)) | (~always19(s104)) | always19(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s76) | (~trans(s104, s76))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14024])).
% 2.48/2.41 tff(14026,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s76)) | (~always19(s104)) | always19(s76))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s76) | (~trans(s104, s76)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14025, 14023])).
% 2.48/2.41 tff(14027,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s76)) | (~always19(s104)) | always19(s76))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14028,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s76) | (~trans(s104, s76))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14027, 14026])).
% 2.48/2.41 tff(14029,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14028, 12508, 8567, 13586, 8786])).
% 2.48/2.41 tff(14030,plain,(~trans(s104, s76)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(14031,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s69) | (~trans(s104, s69)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s69) | (~trans(s104, s69)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14032,plain,
% 2.48/2.41 (((~trans(s104, s69)) | (~always19(s104)) | always19(s69)) <=> ((~always19(s104)) | always19(s69) | (~trans(s104, s69)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14033,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s69)) | (~always19(s104)) | always19(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s69) | (~trans(s104, s69))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14032])).
% 2.48/2.41 tff(14034,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s69)) | (~always19(s104)) | always19(s69))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s69) | (~trans(s104, s69)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14033, 14031])).
% 2.48/2.41 tff(14035,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s69)) | (~always19(s104)) | always19(s69))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14036,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s69) | (~trans(s104, s69))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14035, 14034])).
% 2.48/2.41 tff(14037,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14036, 12519, 8567, 13586, 8843])).
% 2.48/2.41 tff(14038,plain,(~trans(s104, s69)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(14039,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s5) | (~trans(s104, s5)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s5) | (~trans(s104, s5)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14040,plain,
% 2.48/2.41 (((~trans(s104, s5)) | (~always19(s104)) | always19(s5)) <=> ((~always19(s104)) | always19(s5) | (~trans(s104, s5)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14041,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s5)) | (~always19(s104)) | always19(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s5) | (~trans(s104, s5))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14040])).
% 2.48/2.41 tff(14042,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s5)) | (~always19(s104)) | always19(s5))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s5) | (~trans(s104, s5)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14041, 14039])).
% 2.48/2.41 tff(14043,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s5)) | (~always19(s104)) | always19(s5))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14044,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s5) | (~trans(s104, s5))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14043, 14042])).
% 2.48/2.41 tff(14045,plain,
% 2.48/2.41 ($false),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14044, 12530, 8567, 13586, 9364])).
% 2.48/2.41 tff(14046,plain,(~trans(s104, s5)), inference(lemma,lemma(discharge,[]))).
% 2.48/2.41 tff(14047,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s51, s52)) | (~always19(s51)) | always19(s52))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s51, s52)) | (~always19(s51)) | always19(s52))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14048,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s51, s52)) | (~always19(s51)) | always19(s52))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14049,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s51, s52)) | (~always19(s51)) | always19(s52)),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14048, 14047])).
% 2.48/2.41 tff(14050,plain,
% 2.48/2.41 ((~always19(s51)) | always19(s52)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14049, 8567, 4535])).
% 2.48/2.41 tff(14051,plain,
% 2.48/2.41 (~always19(s51)),
% 2.48/2.41 inference(unit_resolution,[status(thm)],[14050, 8984])).
% 2.48/2.41 tff(14052,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s51) | (~trans(s104, s51)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s51) | (~trans(s104, s51)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14053,plain,
% 2.48/2.41 (((~trans(s104, s51)) | (~always19(s104)) | always19(s51)) <=> ((~always19(s104)) | always19(s51) | (~trans(s104, s51)))),
% 2.48/2.41 inference(rewrite,[status(thm)],[])).
% 2.48/2.41 tff(14054,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s51)) | (~always19(s104)) | always19(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s51) | (~trans(s104, s51))))),
% 2.48/2.41 inference(monotonicity,[status(thm)],[14053])).
% 2.48/2.41 tff(14055,plain,
% 2.48/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s51)) | (~always19(s104)) | always19(s51))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s51) | (~trans(s104, s51)))),
% 2.48/2.41 inference(transitivity,[status(thm)],[14054, 14052])).
% 2.48/2.41 tff(14056,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s51)) | (~always19(s104)) | always19(s51))),
% 2.48/2.41 inference(quant_inst,[status(thm)],[])).
% 2.48/2.41 tff(14057,plain,
% 2.48/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s51) | (~trans(s104, s51))),
% 2.48/2.41 inference(modus_ponens,[status(thm)],[14056, 14055])).
% 2.49/2.41 tff(14058,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14057, 12541, 8567, 13586, 14051])).
% 2.49/2.41 tff(14059,plain,(~trans(s104, s51)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14060,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s58) | (~trans(s104, s58)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s58) | (~trans(s104, s58)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14061,plain,
% 2.49/2.41 (((~trans(s104, s58)) | (~always19(s104)) | always19(s58)) <=> ((~always19(s104)) | always19(s58) | (~trans(s104, s58)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14062,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s58)) | (~always19(s104)) | always19(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s58) | (~trans(s104, s58))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14061])).
% 2.49/2.41 tff(14063,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s58)) | (~always19(s104)) | always19(s58))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s58) | (~trans(s104, s58)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14062, 14060])).
% 2.49/2.41 tff(14064,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s58)) | (~always19(s104)) | always19(s58))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14065,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s58) | (~trans(s104, s58))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14064, 14063])).
% 2.49/2.41 tff(14066,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14065, 12552, 8567, 13586, 8937])).
% 2.49/2.41 tff(14067,plain,(~trans(s104, s58)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14068,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s49) | (~trans(s104, s49)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s49) | (~trans(s104, s49)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14069,plain,
% 2.49/2.41 (((~trans(s104, s49)) | (~always19(s104)) | always19(s49)) <=> ((~always19(s104)) | always19(s49) | (~trans(s104, s49)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14070,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s49)) | (~always19(s104)) | always19(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s49) | (~trans(s104, s49))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14069])).
% 2.49/2.41 tff(14071,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s49)) | (~always19(s104)) | always19(s49))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s49) | (~trans(s104, s49)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14070, 14068])).
% 2.49/2.41 tff(14072,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s49)) | (~always19(s104)) | always19(s49))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14073,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s49) | (~trans(s104, s49))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14072, 14071])).
% 2.49/2.41 tff(14074,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14073, 12563, 8567, 13586, 9008])).
% 2.49/2.41 tff(14075,plain,(~trans(s104, s49)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14076,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s59, s60)) | (~always19(s59)) | always19(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s59, s60)) | (~always19(s59)) | always19(s60))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14077,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s59, s60)) | (~always19(s59)) | always19(s60))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14078,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s59, s60)) | (~always19(s59)) | always19(s60)),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14077, 14076])).
% 2.49/2.41 tff(14079,plain,
% 2.49/2.41 ((~always19(s59)) | always19(s60)),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14078, 8567, 5163])).
% 2.49/2.41 tff(14080,plain,
% 2.49/2.41 (~always19(s59)),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14079, 8918])).
% 2.49/2.41 tff(14081,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s59) | (~trans(s104, s59)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s59) | (~trans(s104, s59)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14082,plain,
% 2.49/2.41 (((~trans(s104, s59)) | (~always19(s104)) | always19(s59)) <=> ((~always19(s104)) | always19(s59) | (~trans(s104, s59)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14083,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s59)) | (~always19(s104)) | always19(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s59) | (~trans(s104, s59))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14082])).
% 2.49/2.41 tff(14084,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s59)) | (~always19(s104)) | always19(s59))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s59) | (~trans(s104, s59)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14083, 14081])).
% 2.49/2.41 tff(14085,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s59)) | (~always19(s104)) | always19(s59))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14086,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s59) | (~trans(s104, s59))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14085, 14084])).
% 2.49/2.41 tff(14087,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14086, 12574, 8567, 13586, 14080])).
% 2.49/2.41 tff(14088,plain,(~trans(s104, s59)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14089,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s60) | (~trans(s104, s60)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s60) | (~trans(s104, s60)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14090,plain,
% 2.49/2.41 (((~trans(s104, s60)) | (~always19(s104)) | always19(s60)) <=> ((~always19(s104)) | always19(s60) | (~trans(s104, s60)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14091,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s60)) | (~always19(s104)) | always19(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s60) | (~trans(s104, s60))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14090])).
% 2.49/2.41 tff(14092,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s60)) | (~always19(s104)) | always19(s60))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s60) | (~trans(s104, s60)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14091, 14089])).
% 2.49/2.41 tff(14093,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s60)) | (~always19(s104)) | always19(s60))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14094,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s60) | (~trans(s104, s60))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14093, 14092])).
% 2.49/2.41 tff(14095,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14094, 12585, 8567, 13586, 8918])).
% 2.49/2.41 tff(14096,plain,(~trans(s104, s60)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14097,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s53) | (~trans(s104, s53)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s53) | (~trans(s104, s53)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14098,plain,
% 2.49/2.41 (((~trans(s104, s53)) | (~always19(s104)) | always19(s53)) <=> ((~always19(s104)) | always19(s53) | (~trans(s104, s53)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14099,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s53)) | (~always19(s104)) | always19(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s53) | (~trans(s104, s53))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14098])).
% 2.49/2.41 tff(14100,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s53)) | (~always19(s104)) | always19(s53))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s53) | (~trans(s104, s53)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14099, 14097])).
% 2.49/2.41 tff(14101,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s53)) | (~always19(s104)) | always19(s53))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14102,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s53) | (~trans(s104, s53))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14101, 14100])).
% 2.49/2.41 tff(14103,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14102, 12596, 8567, 13586, 8975])).
% 2.49/2.41 tff(14104,plain,(~trans(s104, s53)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14105,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s8) | (~trans(s104, s8)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s8) | (~trans(s104, s8)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14106,plain,
% 2.49/2.41 (((~trans(s104, s8)) | (~always19(s104)) | always19(s8)) <=> ((~always19(s104)) | always19(s8) | (~trans(s104, s8)))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14107,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s8)) | (~always19(s104)) | always19(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s8) | (~trans(s104, s8))))),
% 2.49/2.41 inference(monotonicity,[status(thm)],[14106])).
% 2.49/2.41 tff(14108,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s8)) | (~always19(s104)) | always19(s8))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s8) | (~trans(s104, s8)))),
% 2.49/2.41 inference(transitivity,[status(thm)],[14107, 14105])).
% 2.49/2.41 tff(14109,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s8)) | (~always19(s104)) | always19(s8))),
% 2.49/2.41 inference(quant_inst,[status(thm)],[])).
% 2.49/2.41 tff(14110,plain,
% 2.49/2.41 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s8) | (~trans(s104, s8))),
% 2.49/2.41 inference(modus_ponens,[status(thm)],[14109, 14108])).
% 2.49/2.41 tff(14111,plain,
% 2.49/2.41 ($false),
% 2.49/2.41 inference(unit_resolution,[status(thm)],[14110, 12607, 8567, 13586, 9340])).
% 2.49/2.41 tff(14112,plain,(~trans(s104, s8)), inference(lemma,lemma(discharge,[]))).
% 2.49/2.41 tff(14113,plain,
% 2.49/2.41 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s71, s72)) | (~always19(s71)) | always19(s72))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s71, s72)) | (~always19(s71)) | always19(s72))),
% 2.49/2.41 inference(rewrite,[status(thm)],[])).
% 2.49/2.41 tff(14114,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s71, s72)) | (~always19(s71)) | always19(s72))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14115,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s71, s72)) | (~always19(s71)) | always19(s72)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14114, 14113])).
% 2.50/2.42 tff(14116,plain,
% 2.50/2.42 ((~always19(s71)) | always19(s72)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14115, 8567, 6086])).
% 2.50/2.42 tff(14117,plain,
% 2.50/2.42 (~always19(s71)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14116, 8819])).
% 2.50/2.42 tff(14118,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s71) | (~trans(s104, s71)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s71) | (~trans(s104, s71)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14119,plain,
% 2.50/2.42 (((~trans(s104, s71)) | (~always19(s104)) | always19(s71)) <=> ((~always19(s104)) | always19(s71) | (~trans(s104, s71)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14120,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s71)) | (~always19(s104)) | always19(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s71) | (~trans(s104, s71))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14119])).
% 2.50/2.42 tff(14121,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s71)) | (~always19(s104)) | always19(s71))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s71) | (~trans(s104, s71)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14120, 14118])).
% 2.50/2.42 tff(14122,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s71)) | (~always19(s104)) | always19(s71))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14123,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s71) | (~trans(s104, s71))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14122, 14121])).
% 2.50/2.42 tff(14124,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14123, 12618, 8567, 13586, 14117])).
% 2.50/2.42 tff(14125,plain,(~trans(s104, s71)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14126,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s17) | (~trans(s104, s17)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s17) | (~trans(s104, s17)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14127,plain,
% 2.50/2.42 (((~trans(s104, s17)) | (~always19(s104)) | always19(s17)) <=> ((~always19(s104)) | always19(s17) | (~trans(s104, s17)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14128,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s17)) | (~always19(s104)) | always19(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s17) | (~trans(s104, s17))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14127])).
% 2.50/2.42 tff(14129,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s17)) | (~always19(s104)) | always19(s17))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s17) | (~trans(s104, s17)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14128, 14126])).
% 2.50/2.42 tff(14130,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s17)) | (~always19(s104)) | always19(s17))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14131,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s17) | (~trans(s104, s17))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14130, 14129])).
% 2.50/2.42 tff(14132,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14131, 12629, 8567, 13586, 9265])).
% 2.50/2.42 tff(14133,plain,(~trans(s104, s17)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14134,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s61) | (~trans(s104, s61)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s61) | (~trans(s104, s61)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14135,plain,
% 2.50/2.42 (((~trans(s104, s61)) | (~always19(s104)) | always19(s61)) <=> ((~always19(s104)) | always19(s61) | (~trans(s104, s61)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14136,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s61)) | (~always19(s104)) | always19(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s61) | (~trans(s104, s61))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14135])).
% 2.50/2.42 tff(14137,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s61)) | (~always19(s104)) | always19(s61))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s61) | (~trans(s104, s61)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14136, 14134])).
% 2.50/2.42 tff(14138,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s61)) | (~always19(s104)) | always19(s61))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14139,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s61) | (~trans(s104, s61))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14138, 14137])).
% 2.50/2.42 tff(14140,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14139, 12640, 8567, 13586, 8909])).
% 2.50/2.42 tff(14141,plain,(~trans(s104, s61)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14142,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s67, s68)) | (~always19(s67)) | always19(s68))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s67, s68)) | (~always19(s67)) | always19(s68))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14143,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s67, s68)) | (~always19(s67)) | always19(s68))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14144,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s67, s68)) | (~always19(s67)) | always19(s68)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14143, 14142])).
% 2.50/2.42 tff(14145,plain,
% 2.50/2.42 ((~always19(s67)) | always19(s68)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14144, 8567, 5791])).
% 2.50/2.42 tff(14146,plain,
% 2.50/2.42 (~always19(s67)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14145, 8852])).
% 2.50/2.42 tff(14147,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s67) | (~trans(s104, s67)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s67) | (~trans(s104, s67)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14148,plain,
% 2.50/2.42 (((~trans(s104, s67)) | (~always19(s104)) | always19(s67)) <=> ((~always19(s104)) | always19(s67) | (~trans(s104, s67)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14149,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s67)) | (~always19(s104)) | always19(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s67) | (~trans(s104, s67))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14148])).
% 2.50/2.42 tff(14150,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s67)) | (~always19(s104)) | always19(s67))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s67) | (~trans(s104, s67)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14149, 14147])).
% 2.50/2.42 tff(14151,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s67)) | (~always19(s104)) | always19(s67))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14152,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s67) | (~trans(s104, s67))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14151, 14150])).
% 2.50/2.42 tff(14153,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14152, 12651, 8567, 13586, 14146])).
% 2.50/2.42 tff(14154,plain,(~trans(s104, s67)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14155,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s65) | (~trans(s104, s65)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s65) | (~trans(s104, s65)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14156,plain,
% 2.50/2.42 (((~trans(s104, s65)) | (~always19(s104)) | always19(s65)) <=> ((~always19(s104)) | always19(s65) | (~trans(s104, s65)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14157,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s65)) | (~always19(s104)) | always19(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s65) | (~trans(s104, s65))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14156])).
% 2.50/2.42 tff(14158,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s65)) | (~always19(s104)) | always19(s65))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s65) | (~trans(s104, s65)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14157, 14155])).
% 2.50/2.42 tff(14159,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s65)) | (~always19(s104)) | always19(s65))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14160,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s65) | (~trans(s104, s65))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14159, 14158])).
% 2.50/2.42 tff(14161,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14160, 12662, 8567, 13586, 8876])).
% 2.50/2.42 tff(14162,plain,(~trans(s104, s65)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14163,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s43, s44)) | (~always19(s43)) | always19(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s43, s44)) | (~always19(s43)) | always19(s44))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14164,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s43, s44)) | (~always19(s43)) | always19(s44))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14165,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s43, s44)) | (~always19(s43)) | always19(s44)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14164, 14163])).
% 2.50/2.42 tff(14166,plain,
% 2.50/2.42 ((~always19(s43)) | always19(s44)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14165, 8567, 3907])).
% 2.50/2.42 tff(14167,plain,
% 2.50/2.42 (~always19(s43)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14166, 9050])).
% 2.50/2.42 tff(14168,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s43) | (~trans(s104, s43)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s43) | (~trans(s104, s43)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14169,plain,
% 2.50/2.42 (((~trans(s104, s43)) | (~always19(s104)) | always19(s43)) <=> ((~always19(s104)) | always19(s43) | (~trans(s104, s43)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14170,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s43)) | (~always19(s104)) | always19(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s43) | (~trans(s104, s43))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14169])).
% 2.50/2.42 tff(14171,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s43)) | (~always19(s104)) | always19(s43))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s43) | (~trans(s104, s43)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14170, 14168])).
% 2.50/2.42 tff(14172,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s43)) | (~always19(s104)) | always19(s43))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14173,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s43) | (~trans(s104, s43))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14172, 14171])).
% 2.50/2.42 tff(14174,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14173, 12673, 8567, 13586, 14167])).
% 2.50/2.42 tff(14175,plain,(~trans(s104, s43)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14176,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s83, s84)) | (~always19(s83)) | always19(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s83, s84)) | (~always19(s83)) | always19(s84))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14177,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s83, s84)) | (~always19(s83)) | always19(s84))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14178,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s83, s84)) | (~always19(s83)) | always19(s84)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14177, 14176])).
% 2.50/2.42 tff(14179,plain,
% 2.50/2.42 ((~always19(s83)) | always19(s84)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14178, 8567, 7047])).
% 2.50/2.42 tff(14180,plain,
% 2.50/2.42 (~always19(s83)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14179, 8720])).
% 2.50/2.42 tff(14181,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s83) | (~trans(s104, s83)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s83) | (~trans(s104, s83)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14182,plain,
% 2.50/2.42 (((~trans(s104, s83)) | (~always19(s104)) | always19(s83)) <=> ((~always19(s104)) | always19(s83) | (~trans(s104, s83)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14183,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s83)) | (~always19(s104)) | always19(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s83) | (~trans(s104, s83))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14182])).
% 2.50/2.42 tff(14184,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s83)) | (~always19(s104)) | always19(s83))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s83) | (~trans(s104, s83)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14183, 14181])).
% 2.50/2.42 tff(14185,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s83)) | (~always19(s104)) | always19(s83))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14186,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s83) | (~trans(s104, s83))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14185, 14184])).
% 2.50/2.42 tff(14187,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14186, 12684, 8567, 13586, 14180])).
% 2.50/2.42 tff(14188,plain,(~trans(s104, s83)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14189,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s0, s1)) | (~always19(s0)) | always19(s1))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s0, s1)) | (~always19(s0)) | always19(s1))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14190,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s0, s1)) | (~always19(s0)) | always19(s1))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14191,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s0, s1)) | (~always19(s0)) | always19(s1)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14190, 14189])).
% 2.50/2.42 tff(14192,plain,
% 2.50/2.42 ((~always19(s0)) | always19(s1)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14191, 8567, 46])).
% 2.50/2.42 tff(14193,plain,
% 2.50/2.42 (~always19(s0)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14192, 9401])).
% 2.50/2.42 tff(14194,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s0) | (~trans(s104, s0)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s0) | (~trans(s104, s0)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14195,plain,
% 2.50/2.42 (((~trans(s104, s0)) | (~always19(s104)) | always19(s0)) <=> ((~always19(s104)) | always19(s0) | (~trans(s104, s0)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14196,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s0)) | (~always19(s104)) | always19(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s0) | (~trans(s104, s0))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14195])).
% 2.50/2.42 tff(14197,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s0)) | (~always19(s104)) | always19(s0))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s0) | (~trans(s104, s0)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14196, 14194])).
% 2.50/2.42 tff(14198,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s0)) | (~always19(s104)) | always19(s0))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14199,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s0) | (~trans(s104, s0))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14198, 14197])).
% 2.50/2.42 tff(14200,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14199, 12705, 8567, 13586, 14193])).
% 2.50/2.42 tff(14201,plain,(~trans(s104, s0)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14202,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s50) | (~trans(s104, s50)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s50) | (~trans(s104, s50)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14203,plain,
% 2.50/2.42 (((~trans(s104, s50)) | (~always19(s104)) | always19(s50)) <=> ((~always19(s104)) | always19(s50) | (~trans(s104, s50)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14204,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s50)) | (~always19(s104)) | always19(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s50) | (~trans(s104, s50))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14203])).
% 2.50/2.42 tff(14205,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s50)) | (~always19(s104)) | always19(s50))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s50) | (~trans(s104, s50)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14204, 14202])).
% 2.50/2.42 tff(14206,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s50)) | (~always19(s104)) | always19(s50))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14207,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s50) | (~trans(s104, s50))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14206, 14205])).
% 2.50/2.42 tff(14208,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14207, 12716, 8567, 13586, 9003])).
% 2.50/2.42 tff(14209,plain,(~trans(s104, s50)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14210,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s36) | (~trans(s104, s36)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s36) | (~trans(s104, s36)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14211,plain,
% 2.50/2.42 (((~trans(s104, s36)) | (~always19(s104)) | always19(s36)) <=> ((~always19(s104)) | always19(s36) | (~trans(s104, s36)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14212,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s36)) | (~always19(s104)) | always19(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s36) | (~trans(s104, s36))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14211])).
% 2.50/2.42 tff(14213,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s36)) | (~always19(s104)) | always19(s36))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s36) | (~trans(s104, s36)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14212, 14210])).
% 2.50/2.42 tff(14214,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s36)) | (~always19(s104)) | always19(s36))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14215,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s36) | (~trans(s104, s36))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14214, 14213])).
% 2.50/2.42 tff(14216,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14215, 12727, 8567, 13586, 9109])).
% 2.50/2.42 tff(14217,plain,(~trans(s104, s36)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14218,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s41) | (~trans(s104, s41)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s41) | (~trans(s104, s41)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14219,plain,
% 2.50/2.42 (((~trans(s104, s41)) | (~always19(s104)) | always19(s41)) <=> ((~always19(s104)) | always19(s41) | (~trans(s104, s41)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14220,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s41)) | (~always19(s104)) | always19(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s41) | (~trans(s104, s41))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14219])).
% 2.50/2.42 tff(14221,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s41)) | (~always19(s104)) | always19(s41))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s41) | (~trans(s104, s41)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14220, 14218])).
% 2.50/2.42 tff(14222,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s41)) | (~always19(s104)) | always19(s41))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14223,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s41) | (~trans(s104, s41))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14222, 14221])).
% 2.50/2.42 tff(14224,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14223, 12738, 8567, 13586, 9074])).
% 2.50/2.42 tff(14225,plain,(~trans(s104, s41)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14226,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s11, s12)) | (~always19(s11)) | always19(s12))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s11, s12)) | (~always19(s11)) | always19(s12))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14227,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s11, s12)) | (~always19(s11)) | always19(s12))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14228,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s11, s12)) | (~always19(s11)) | always19(s12)),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14227, 14226])).
% 2.50/2.42 tff(14229,plain,
% 2.50/2.42 ((~always19(s11)) | always19(s12)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14228, 8567, 1380])).
% 2.50/2.42 tff(14230,plain,
% 2.50/2.42 (~always19(s11)),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14229, 9307])).
% 2.50/2.42 tff(14231,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s11) | (~trans(s104, s11)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s11) | (~trans(s104, s11)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14232,plain,
% 2.50/2.42 (((~trans(s104, s11)) | (~always19(s104)) | always19(s11)) <=> ((~always19(s104)) | always19(s11) | (~trans(s104, s11)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14233,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s11)) | (~always19(s104)) | always19(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s11) | (~trans(s104, s11))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14232])).
% 2.50/2.42 tff(14234,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s11)) | (~always19(s104)) | always19(s11))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s11) | (~trans(s104, s11)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14233, 14231])).
% 2.50/2.42 tff(14235,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s11)) | (~always19(s104)) | always19(s11))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14236,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s11) | (~trans(s104, s11))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14235, 14234])).
% 2.50/2.42 tff(14237,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14236, 12749, 8567, 13586, 14230])).
% 2.50/2.42 tff(14238,plain,(~trans(s104, s11)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14239,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s89) | (~trans(s104, s89)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s89) | (~trans(s104, s89)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14240,plain,
% 2.50/2.42 (((~trans(s104, s89)) | (~always19(s104)) | always19(s89)) <=> ((~always19(s104)) | always19(s89) | (~trans(s104, s89)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14241,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s89)) | (~always19(s104)) | always19(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s89) | (~trans(s104, s89))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14240])).
% 2.50/2.42 tff(14242,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s89)) | (~always19(s104)) | always19(s89))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s89) | (~trans(s104, s89)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14241, 14239])).
% 2.50/2.42 tff(14243,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s89)) | (~always19(s104)) | always19(s89))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14244,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s89) | (~trans(s104, s89))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14243, 14242])).
% 2.50/2.42 tff(14245,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14244, 12760, 8567, 13586, 8678])).
% 2.50/2.42 tff(14246,plain,(~trans(s104, s89)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14247,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s101) | (~trans(s104, s101)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s101) | (~trans(s104, s101)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14248,plain,
% 2.50/2.42 (((~trans(s104, s101)) | (~always19(s104)) | always19(s101)) <=> ((~always19(s104)) | always19(s101) | (~trans(s104, s101)))),
% 2.50/2.42 inference(rewrite,[status(thm)],[])).
% 2.50/2.42 tff(14249,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s101)) | (~always19(s104)) | always19(s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s101) | (~trans(s104, s101))))),
% 2.50/2.42 inference(monotonicity,[status(thm)],[14248])).
% 2.50/2.42 tff(14250,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s101)) | (~always19(s104)) | always19(s101))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s101) | (~trans(s104, s101)))),
% 2.50/2.42 inference(transitivity,[status(thm)],[14249, 14247])).
% 2.50/2.42 tff(14251,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s101)) | (~always19(s104)) | always19(s101))),
% 2.50/2.42 inference(quant_inst,[status(thm)],[])).
% 2.50/2.42 tff(14252,plain,
% 2.50/2.42 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s101) | (~trans(s104, s101))),
% 2.50/2.42 inference(modus_ponens,[status(thm)],[14251, 14250])).
% 2.50/2.42 tff(14253,plain,
% 2.50/2.42 ($false),
% 2.50/2.42 inference(unit_resolution,[status(thm)],[14252, 12771, 8567, 13586, 8572])).
% 2.50/2.42 tff(14254,plain,(~trans(s104, s101)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.42 tff(14255,plain,
% 2.50/2.42 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s45) | (~trans(s104, s45)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s45) | (~trans(s104, s45)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14256,plain,
% 2.50/2.43 (((~trans(s104, s45)) | (~always19(s104)) | always19(s45)) <=> ((~always19(s104)) | always19(s45) | (~trans(s104, s45)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14257,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s45)) | (~always19(s104)) | always19(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s45) | (~trans(s104, s45))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14256])).
% 2.50/2.43 tff(14258,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s45)) | (~always19(s104)) | always19(s45))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s45) | (~trans(s104, s45)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14257, 14255])).
% 2.50/2.43 tff(14259,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s45)) | (~always19(s104)) | always19(s45))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14260,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s45) | (~trans(s104, s45))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14259, 14258])).
% 2.50/2.43 tff(14261,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14260, 12782, 8567, 13586, 9041])).
% 2.50/2.43 tff(14262,plain,(~trans(s104, s45)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14263,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s82) | (~trans(s104, s82)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s82) | (~trans(s104, s82)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14264,plain,
% 2.50/2.43 (((~trans(s104, s82)) | (~always19(s104)) | always19(s82)) <=> ((~always19(s104)) | always19(s82) | (~trans(s104, s82)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14265,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s82)) | (~always19(s104)) | always19(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s82) | (~trans(s104, s82))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14264])).
% 2.50/2.43 tff(14266,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s82)) | (~always19(s104)) | always19(s82))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s82) | (~trans(s104, s82)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14265, 14263])).
% 2.50/2.43 tff(14267,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s82)) | (~always19(s104)) | always19(s82))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14268,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s82) | (~trans(s104, s82))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14267, 14266])).
% 2.50/2.43 tff(14269,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14268, 12793, 8567, 13586, 8739])).
% 2.50/2.43 tff(14270,plain,(~trans(s104, s82)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14271,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s98) | (~trans(s104, s98)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s98) | (~trans(s104, s98)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14272,plain,
% 2.50/2.43 (((~trans(s104, s98)) | (~always19(s104)) | always19(s98)) <=> ((~always19(s104)) | always19(s98) | (~trans(s104, s98)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14273,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s98)) | (~always19(s104)) | always19(s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s98) | (~trans(s104, s98))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14272])).
% 2.50/2.43 tff(14274,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s98)) | (~always19(s104)) | always19(s98))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s98) | (~trans(s104, s98)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14273, 14271])).
% 2.50/2.43 tff(14275,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s98)) | (~always19(s104)) | always19(s98))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14276,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s98) | (~trans(s104, s98))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14275, 14274])).
% 2.50/2.43 tff(14277,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14276, 12804, 8567, 13586, 8607])).
% 2.50/2.43 tff(14278,plain,(~trans(s104, s98)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14279,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s3, s4)) | (~always19(s3)) | always19(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s3, s4)) | (~always19(s3)) | always19(s4))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14280,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s3, s4)) | (~always19(s3)) | always19(s4))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14281,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s3, s4)) | (~always19(s3)) | always19(s4)),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14280, 14279])).
% 2.50/2.43 tff(14282,plain,
% 2.50/2.43 ((~always19(s3)) | always19(s4)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14281, 8567, 603])).
% 2.50/2.43 tff(14283,plain,
% 2.50/2.43 (~always19(s3)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14282, 9373])).
% 2.50/2.43 tff(14284,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s3) | (~trans(s104, s3)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s3) | (~trans(s104, s3)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14285,plain,
% 2.50/2.43 (((~trans(s104, s3)) | (~always19(s104)) | always19(s3)) <=> ((~always19(s104)) | always19(s3) | (~trans(s104, s3)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14286,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s3)) | (~always19(s104)) | always19(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s3) | (~trans(s104, s3))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14285])).
% 2.50/2.43 tff(14287,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s3)) | (~always19(s104)) | always19(s3))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s3) | (~trans(s104, s3)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14286, 14284])).
% 2.50/2.43 tff(14288,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s3)) | (~always19(s104)) | always19(s3))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14289,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s3) | (~trans(s104, s3))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14288, 14287])).
% 2.50/2.43 tff(14290,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14289, 12815, 8567, 13586, 14283])).
% 2.50/2.43 tff(14291,plain,(~trans(s104, s3)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14292,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s18) | (~trans(s104, s18)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s18) | (~trans(s104, s18)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14293,plain,
% 2.50/2.43 (((~trans(s104, s18)) | (~always19(s104)) | always19(s18)) <=> ((~always19(s104)) | always19(s18) | (~trans(s104, s18)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14294,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s18)) | (~always19(s104)) | always19(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s18) | (~trans(s104, s18))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14293])).
% 2.50/2.43 tff(14295,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s18)) | (~always19(s104)) | always19(s18))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s18) | (~trans(s104, s18)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14294, 14292])).
% 2.50/2.43 tff(14296,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s18)) | (~always19(s104)) | always19(s18))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14297,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s18) | (~trans(s104, s18))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14296, 14295])).
% 2.50/2.43 tff(14298,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14297, 12826, 8567, 13586, 9260])).
% 2.50/2.43 tff(14299,plain,(~trans(s104, s18)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14300,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s86) | (~trans(s104, s86)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s86) | (~trans(s104, s86)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14301,plain,
% 2.50/2.43 (((~trans(s104, s86)) | (~always19(s104)) | always19(s86)) <=> ((~always19(s104)) | always19(s86) | (~trans(s104, s86)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14302,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s86)) | (~always19(s104)) | always19(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s86) | (~trans(s104, s86))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14301])).
% 2.50/2.43 tff(14303,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s86)) | (~always19(s104)) | always19(s86))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s86) | (~trans(s104, s86)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14302, 14300])).
% 2.50/2.43 tff(14304,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s86)) | (~always19(s104)) | always19(s86))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14305,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s86) | (~trans(s104, s86))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14304, 14303])).
% 2.50/2.43 tff(14306,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14305, 12837, 8567, 13586, 8706])).
% 2.50/2.43 tff(14307,plain,(~trans(s104, s86)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14308,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s92) | (~trans(s104, s92)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s92) | (~trans(s104, s92)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14309,plain,
% 2.50/2.43 (((~trans(s104, s92)) | (~always19(s104)) | always19(s92)) <=> ((~always19(s104)) | always19(s92) | (~trans(s104, s92)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14310,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s92)) | (~always19(s104)) | always19(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s92) | (~trans(s104, s92))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14309])).
% 2.50/2.43 tff(14311,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s92)) | (~always19(s104)) | always19(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s92) | (~trans(s104, s92)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14310, 14308])).
% 2.50/2.43 tff(14312,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s92)) | (~always19(s104)) | always19(s92))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14313,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s92) | (~trans(s104, s92))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14312, 14311])).
% 2.50/2.43 tff(14314,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14313, 12848, 8567, 13586, 8654])).
% 2.50/2.43 tff(14315,plain,(~trans(s104, s92)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14316,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s14) | (~trans(s104, s14)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s14) | (~trans(s104, s14)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14317,plain,
% 2.50/2.43 (((~trans(s104, s14)) | (~always19(s104)) | always19(s14)) <=> ((~always19(s104)) | always19(s14) | (~trans(s104, s14)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14318,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s14)) | (~always19(s104)) | always19(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s14) | (~trans(s104, s14))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14317])).
% 2.50/2.43 tff(14319,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s14)) | (~always19(s104)) | always19(s14))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s14) | (~trans(s104, s14)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14318, 14316])).
% 2.50/2.43 tff(14320,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s14)) | (~always19(s104)) | always19(s14))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14321,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s14) | (~trans(s104, s14))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14320, 14319])).
% 2.50/2.43 tff(14322,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14321, 12859, 8567, 13586, 9293])).
% 2.50/2.43 tff(14323,plain,(~trans(s104, s14)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14324,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s77) | (~trans(s104, s77)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s77) | (~trans(s104, s77)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14325,plain,
% 2.50/2.43 (((~trans(s104, s77)) | (~always19(s104)) | always19(s77)) <=> ((~always19(s104)) | always19(s77) | (~trans(s104, s77)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14326,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s77)) | (~always19(s104)) | always19(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s77) | (~trans(s104, s77))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14325])).
% 2.50/2.43 tff(14327,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s77)) | (~always19(s104)) | always19(s77))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s77) | (~trans(s104, s77)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14326, 14324])).
% 2.50/2.43 tff(14328,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s77)) | (~always19(s104)) | always19(s77))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14329,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s77) | (~trans(s104, s77))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14328, 14327])).
% 2.50/2.43 tff(14330,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14329, 12870, 8567, 13586, 8777])).
% 2.50/2.43 tff(14331,plain,(~trans(s104, s77)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14332,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s46) | (~trans(s104, s46)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s46) | (~trans(s104, s46)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14333,plain,
% 2.50/2.43 (((~trans(s104, s46)) | (~always19(s104)) | always19(s46)) <=> ((~always19(s104)) | always19(s46) | (~trans(s104, s46)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14334,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s46)) | (~always19(s104)) | always19(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s46) | (~trans(s104, s46))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14333])).
% 2.50/2.43 tff(14335,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s46)) | (~always19(s104)) | always19(s46))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s46) | (~trans(s104, s46)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14334, 14332])).
% 2.50/2.43 tff(14336,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s46)) | (~always19(s104)) | always19(s46))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14337,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s46) | (~trans(s104, s46))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14336, 14335])).
% 2.50/2.43 tff(14338,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14337, 12881, 8567, 13586, 9036])).
% 2.50/2.43 tff(14339,plain,(~trans(s104, s46)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14340,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s84) | (~trans(s104, s84)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s84) | (~trans(s104, s84)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14341,plain,
% 2.50/2.43 (((~trans(s104, s84)) | (~always19(s104)) | always19(s84)) <=> ((~always19(s104)) | always19(s84) | (~trans(s104, s84)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14342,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s84)) | (~always19(s104)) | always19(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s84) | (~trans(s104, s84))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14341])).
% 2.50/2.43 tff(14343,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s84)) | (~always19(s104)) | always19(s84))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s84) | (~trans(s104, s84)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14342, 14340])).
% 2.50/2.43 tff(14344,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s84)) | (~always19(s104)) | always19(s84))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14345,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s84) | (~trans(s104, s84))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14344, 14343])).
% 2.50/2.43 tff(14346,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14345, 12892, 8567, 13586, 8720])).
% 2.50/2.43 tff(14347,plain,(~trans(s104, s84)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14348,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s95, s96)) | (~always19(s95)) | always19(s96))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s95, s96)) | (~always19(s95)) | always19(s96))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14349,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s95, s96)) | (~always19(s95)) | always19(s96))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14350,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s95, s96)) | (~always19(s95)) | always19(s96)),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14349, 14348])).
% 2.50/2.43 tff(14351,plain,
% 2.50/2.43 ((~always19(s95)) | always19(s96)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14350, 8567, 7970])).
% 2.50/2.43 tff(14352,plain,
% 2.50/2.43 (~always19(s95)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14351, 8621])).
% 2.50/2.43 tff(14353,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s95) | (~trans(s104, s95)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s95) | (~trans(s104, s95)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14354,plain,
% 2.50/2.43 (((~trans(s104, s95)) | (~always19(s104)) | always19(s95)) <=> ((~always19(s104)) | always19(s95) | (~trans(s104, s95)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14355,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s95)) | (~always19(s104)) | always19(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s95) | (~trans(s104, s95))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14354])).
% 2.50/2.43 tff(14356,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s95)) | (~always19(s104)) | always19(s95))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s95) | (~trans(s104, s95)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14355, 14353])).
% 2.50/2.43 tff(14357,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s95)) | (~always19(s104)) | always19(s95))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14358,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s95) | (~trans(s104, s95))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14357, 14356])).
% 2.50/2.43 tff(14359,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14358, 12903, 8567, 13586, 14352])).
% 2.50/2.43 tff(14360,plain,(~trans(s104, s95)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14361,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s87, s88)) | (~always19(s87)) | always19(s88))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s87, s88)) | (~always19(s87)) | always19(s88))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14362,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s87, s88)) | (~always19(s87)) | always19(s88))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14363,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s87, s88)) | (~always19(s87)) | always19(s88)),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14362, 14361])).
% 2.50/2.43 tff(14364,plain,
% 2.50/2.43 ((~always19(s87)) | always19(s88)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14363, 8567, 7342])).
% 2.50/2.43 tff(14365,plain,
% 2.50/2.43 (~always19(s87)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14364, 8687])).
% 2.50/2.43 tff(14366,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s87) | (~trans(s104, s87)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s87) | (~trans(s104, s87)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14367,plain,
% 2.50/2.43 (((~trans(s104, s87)) | (~always19(s104)) | always19(s87)) <=> ((~always19(s104)) | always19(s87) | (~trans(s104, s87)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14368,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s87)) | (~always19(s104)) | always19(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s87) | (~trans(s104, s87))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14367])).
% 2.50/2.43 tff(14369,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s87)) | (~always19(s104)) | always19(s87))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s87) | (~trans(s104, s87)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14368, 14366])).
% 2.50/2.43 tff(14370,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s87)) | (~always19(s104)) | always19(s87))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14371,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s87) | (~trans(s104, s87))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14370, 14369])).
% 2.50/2.43 tff(14372,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14371, 12914, 8567, 13586, 14365])).
% 2.50/2.43 tff(14373,plain,(~trans(s104, s87)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14374,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s6) | (~trans(s104, s6)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s6) | (~trans(s104, s6)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14375,plain,
% 2.50/2.43 (((~trans(s104, s6)) | (~always19(s104)) | always19(s6)) <=> ((~always19(s104)) | always19(s6) | (~trans(s104, s6)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14376,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s6)) | (~always19(s104)) | always19(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s6) | (~trans(s104, s6))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14375])).
% 2.50/2.43 tff(14377,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s6)) | (~always19(s104)) | always19(s6))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s6) | (~trans(s104, s6)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14376, 14374])).
% 2.50/2.43 tff(14378,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s6)) | (~always19(s104)) | always19(s6))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14379,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s6) | (~trans(s104, s6))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14378, 14377])).
% 2.50/2.43 tff(14380,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14379, 12925, 8567, 13586, 9359])).
% 2.50/2.43 tff(14381,plain,(~trans(s104, s6)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14382,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s47, s48)) | (~always19(s47)) | always19(s48))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s47, s48)) | (~always19(s47)) | always19(s48))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14383,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s47, s48)) | (~always19(s47)) | always19(s48))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14384,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s47, s48)) | (~always19(s47)) | always19(s48)),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14383, 14382])).
% 2.50/2.43 tff(14385,plain,
% 2.50/2.43 ((~always19(s47)) | always19(s48)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14384, 8567, 4202])).
% 2.50/2.43 tff(14386,plain,
% 2.50/2.43 (~always19(s47)),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14385, 9017])).
% 2.50/2.43 tff(14387,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s47) | (~trans(s104, s47)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s47) | (~trans(s104, s47)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14388,plain,
% 2.50/2.43 (((~trans(s104, s47)) | (~always19(s104)) | always19(s47)) <=> ((~always19(s104)) | always19(s47) | (~trans(s104, s47)))),
% 2.50/2.43 inference(rewrite,[status(thm)],[])).
% 2.50/2.43 tff(14389,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s47)) | (~always19(s104)) | always19(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s47) | (~trans(s104, s47))))),
% 2.50/2.43 inference(monotonicity,[status(thm)],[14388])).
% 2.50/2.43 tff(14390,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s47)) | (~always19(s104)) | always19(s47))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s47) | (~trans(s104, s47)))),
% 2.50/2.43 inference(transitivity,[status(thm)],[14389, 14387])).
% 2.50/2.43 tff(14391,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s47)) | (~always19(s104)) | always19(s47))),
% 2.50/2.43 inference(quant_inst,[status(thm)],[])).
% 2.50/2.43 tff(14392,plain,
% 2.50/2.43 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s47) | (~trans(s104, s47))),
% 2.50/2.43 inference(modus_ponens,[status(thm)],[14391, 14390])).
% 2.50/2.43 tff(14393,plain,
% 2.50/2.43 ($false),
% 2.50/2.43 inference(unit_resolution,[status(thm)],[14392, 12936, 8567, 13586, 14386])).
% 2.50/2.43 tff(14394,plain,(~trans(s104, s47)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.43 tff(14395,plain,
% 2.50/2.43 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s79, s80)) | (~always19(s79)) | always19(s80))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s79, s80)) | (~always19(s79)) | always19(s80))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14396,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s79, s80)) | (~always19(s79)) | always19(s80))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14397,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s79, s80)) | (~always19(s79)) | always19(s80)),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14396, 14395])).
% 2.50/2.44 tff(14398,plain,
% 2.50/2.44 ((~always19(s79)) | always19(s80)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14397, 8567, 6714])).
% 2.50/2.44 tff(14399,plain,
% 2.50/2.44 (~always19(s79)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14398, 8753])).
% 2.50/2.44 tff(14400,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s79) | (~trans(s104, s79)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s79) | (~trans(s104, s79)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14401,plain,
% 2.50/2.44 (((~trans(s104, s79)) | (~always19(s104)) | always19(s79)) <=> ((~always19(s104)) | always19(s79) | (~trans(s104, s79)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14402,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s79)) | (~always19(s104)) | always19(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s79) | (~trans(s104, s79))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14401])).
% 2.50/2.44 tff(14403,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s79)) | (~always19(s104)) | always19(s79))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s79) | (~trans(s104, s79)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14402, 14400])).
% 2.50/2.44 tff(14404,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s79)) | (~always19(s104)) | always19(s79))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14405,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s79) | (~trans(s104, s79))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14404, 14403])).
% 2.50/2.44 tff(14406,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14405, 12947, 8567, 13586, 14399])).
% 2.50/2.44 tff(14407,plain,(~trans(s104, s79)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14408,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s30) | (~trans(s104, s30)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s30) | (~trans(s104, s30)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14409,plain,
% 2.50/2.44 (((~trans(s104, s30)) | (~always19(s104)) | always19(s30)) <=> ((~always19(s104)) | always19(s30) | (~trans(s104, s30)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14410,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s30)) | (~always19(s104)) | always19(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s30) | (~trans(s104, s30))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14409])).
% 2.50/2.44 tff(14411,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s30)) | (~always19(s104)) | always19(s30))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s30) | (~trans(s104, s30)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14410, 14408])).
% 2.50/2.44 tff(14412,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s30)) | (~always19(s104)) | always19(s30))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14413,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s30) | (~trans(s104, s30))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14412, 14411])).
% 2.50/2.44 tff(14414,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14413, 12958, 8567, 13586, 9161])).
% 2.50/2.44 tff(14415,plain,(~trans(s104, s30)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14416,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s44) | (~trans(s104, s44)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s44) | (~trans(s104, s44)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14417,plain,
% 2.50/2.44 (((~trans(s104, s44)) | (~always19(s104)) | always19(s44)) <=> ((~always19(s104)) | always19(s44) | (~trans(s104, s44)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14418,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s44)) | (~always19(s104)) | always19(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s44) | (~trans(s104, s44))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14417])).
% 2.50/2.44 tff(14419,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s44)) | (~always19(s104)) | always19(s44))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s44) | (~trans(s104, s44)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14418, 14416])).
% 2.50/2.44 tff(14420,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s44)) | (~always19(s104)) | always19(s44))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14421,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s44) | (~trans(s104, s44))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14420, 14419])).
% 2.50/2.44 tff(14422,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14421, 12969, 8567, 13586, 9050])).
% 2.50/2.44 tff(14423,plain,(~trans(s104, s44)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14424,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s94) | (~trans(s104, s94)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s94) | (~trans(s104, s94)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14425,plain,
% 2.50/2.44 (((~trans(s104, s94)) | (~always19(s104)) | always19(s94)) <=> ((~always19(s104)) | always19(s94) | (~trans(s104, s94)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14426,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s94)) | (~always19(s104)) | always19(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s94) | (~trans(s104, s94))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14425])).
% 2.50/2.44 tff(14427,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s94)) | (~always19(s104)) | always19(s94))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s94) | (~trans(s104, s94)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14426, 14424])).
% 2.50/2.44 tff(14428,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s94)) | (~always19(s104)) | always19(s94))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14429,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s94) | (~trans(s104, s94))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14428, 14427])).
% 2.50/2.44 tff(14430,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14429, 12980, 8567, 13586, 8640])).
% 2.50/2.44 tff(14431,plain,(~trans(s104, s94)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14432,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s90) | (~trans(s104, s90)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s90) | (~trans(s104, s90)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14433,plain,
% 2.50/2.44 (((~trans(s104, s90)) | (~always19(s104)) | always19(s90)) <=> ((~always19(s104)) | always19(s90) | (~trans(s104, s90)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14434,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s90)) | (~always19(s104)) | always19(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s90) | (~trans(s104, s90))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14433])).
% 2.50/2.44 tff(14435,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s90)) | (~always19(s104)) | always19(s90))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s90) | (~trans(s104, s90)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14434, 14432])).
% 2.50/2.44 tff(14436,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s90)) | (~always19(s104)) | always19(s90))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14437,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s90) | (~trans(s104, s90))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14436, 14435])).
% 2.50/2.44 tff(14438,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14437, 12991, 8567, 13586, 8673])).
% 2.50/2.44 tff(14439,plain,(~trans(s104, s90)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14440,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s42) | (~trans(s104, s42)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s42) | (~trans(s104, s42)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14441,plain,
% 2.50/2.44 (((~trans(s104, s42)) | (~always19(s104)) | always19(s42)) <=> ((~always19(s104)) | always19(s42) | (~trans(s104, s42)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14442,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s42)) | (~always19(s104)) | always19(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s42) | (~trans(s104, s42))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14441])).
% 2.50/2.44 tff(14443,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s42)) | (~always19(s104)) | always19(s42))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s42) | (~trans(s104, s42)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14442, 14440])).
% 2.50/2.44 tff(14444,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s42)) | (~always19(s104)) | always19(s42))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14445,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s42) | (~trans(s104, s42))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14444, 14443])).
% 2.50/2.44 tff(14446,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14445, 13002, 8567, 13586, 9069])).
% 2.50/2.44 tff(14447,plain,(~trans(s104, s42)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14448,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s34) | (~trans(s104, s34)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s34) | (~trans(s104, s34)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14449,plain,
% 2.50/2.44 (((~trans(s104, s34)) | (~always19(s104)) | always19(s34)) <=> ((~always19(s104)) | always19(s34) | (~trans(s104, s34)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14450,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s34)) | (~always19(s104)) | always19(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s34) | (~trans(s104, s34))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14449])).
% 2.50/2.44 tff(14451,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s34)) | (~always19(s104)) | always19(s34))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s34) | (~trans(s104, s34)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14450, 14448])).
% 2.50/2.44 tff(14452,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s34)) | (~always19(s104)) | always19(s34))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14453,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s34) | (~trans(s104, s34))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14452, 14451])).
% 2.50/2.44 tff(14454,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14453, 13013, 8567, 13586, 9128])).
% 2.50/2.44 tff(14455,plain,(~trans(s104, s34)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14456,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s100) | (~trans(s104, s100)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s100) | (~trans(s104, s100)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14457,plain,
% 2.50/2.44 (((~trans(s104, s100)) | (~always19(s104)) | always19(s100)) <=> ((~always19(s104)) | always19(s100) | (~trans(s104, s100)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14458,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s100)) | (~always19(s104)) | always19(s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s100) | (~trans(s104, s100))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14457])).
% 2.50/2.44 tff(14459,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s100)) | (~always19(s104)) | always19(s100))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s100) | (~trans(s104, s100)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14458, 14456])).
% 2.50/2.44 tff(14460,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s100)) | (~always19(s104)) | always19(s100))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14461,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s100) | (~trans(s104, s100))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14460, 14459])).
% 2.50/2.44 tff(14462,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14461, 13024, 8567, 13586, 8588])).
% 2.50/2.44 tff(14463,plain,(~trans(s104, s100)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14464,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s26) | (~trans(s104, s26)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s26) | (~trans(s104, s26)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14465,plain,
% 2.50/2.44 (((~trans(s104, s26)) | (~always19(s104)) | always19(s26)) <=> ((~always19(s104)) | always19(s26) | (~trans(s104, s26)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14466,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s26)) | (~always19(s104)) | always19(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s26) | (~trans(s104, s26))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14465])).
% 2.50/2.44 tff(14467,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s26)) | (~always19(s104)) | always19(s26))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s26) | (~trans(s104, s26)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14466, 14464])).
% 2.50/2.44 tff(14468,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s26)) | (~always19(s104)) | always19(s26))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14469,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s26) | (~trans(s104, s26))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14468, 14467])).
% 2.50/2.44 tff(14470,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14469, 13035, 8567, 13586, 9194])).
% 2.50/2.44 tff(14471,plain,(~trans(s104, s26)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14472,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s85) | (~trans(s104, s85)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s85) | (~trans(s104, s85)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14473,plain,
% 2.50/2.44 (((~trans(s104, s85)) | (~always19(s104)) | always19(s85)) <=> ((~always19(s104)) | always19(s85) | (~trans(s104, s85)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14474,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s85)) | (~always19(s104)) | always19(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s85) | (~trans(s104, s85))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14473])).
% 2.50/2.44 tff(14475,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s85)) | (~always19(s104)) | always19(s85))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s85) | (~trans(s104, s85)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14474, 14472])).
% 2.50/2.44 tff(14476,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s85)) | (~always19(s104)) | always19(s85))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14477,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s85) | (~trans(s104, s85))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14476, 14475])).
% 2.50/2.44 tff(14478,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14477, 13046, 8567, 13586, 8711])).
% 2.50/2.44 tff(14479,plain,(~trans(s104, s85)), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14480,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s91, s92)) | (~always19(s91)) | always19(s92))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s91, s92)) | (~always19(s91)) | always19(s92))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14481,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s91, s92)) | (~always19(s91)) | always19(s92))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14482,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~trans(s91, s92)) | (~always19(s91)) | always19(s92)),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14481, 14480])).
% 2.50/2.44 tff(14483,plain,
% 2.50/2.44 ((~always19(s91)) | always19(s92)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14482, 8567, 7675])).
% 2.50/2.44 tff(14484,plain,
% 2.50/2.44 (~always19(s91)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14483, 8654])).
% 2.50/2.44 tff(14485,assumption,(always19(s104)), introduced(assumption)).
% 2.50/2.44 tff(14486,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s91) | (~trans(s104, s91)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s91) | (~trans(s104, s91)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14487,plain,
% 2.50/2.44 (((~trans(s104, s91)) | (~always19(s104)) | always19(s91)) <=> ((~always19(s104)) | always19(s91) | (~trans(s104, s91)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14488,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s91)) | (~always19(s104)) | always19(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s91) | (~trans(s104, s91))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14487])).
% 2.50/2.44 tff(14489,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s91)) | (~always19(s104)) | always19(s91))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s91) | (~trans(s104, s91)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14488, 14486])).
% 2.50/2.44 tff(14490,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s91)) | (~always19(s104)) | always19(s91))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14491,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s91) | (~trans(s104, s91))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14490, 14489])).
% 2.50/2.44 tff(14492,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14491, 11535, 8567, 14485, 14484])).
% 2.50/2.44 tff(14493,plain,((~trans(s104, s91)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14494,plain,
% 2.50/2.44 (~trans(s104, s91)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14493, 13586])).
% 2.50/2.44 tff(14495,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s32) | (~trans(s104, s32)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s32) | (~trans(s104, s32)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14496,plain,
% 2.50/2.44 (((~trans(s104, s32)) | (~always19(s104)) | always19(s32)) <=> ((~always19(s104)) | always19(s32) | (~trans(s104, s32)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14497,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s32)) | (~always19(s104)) | always19(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s32) | (~trans(s104, s32))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14496])).
% 2.50/2.44 tff(14498,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s32)) | (~always19(s104)) | always19(s32))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s32) | (~trans(s104, s32)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14497, 14495])).
% 2.50/2.44 tff(14499,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s32)) | (~always19(s104)) | always19(s32))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14500,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s32) | (~trans(s104, s32))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14499, 14498])).
% 2.50/2.44 tff(14501,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14500, 11626, 8567, 14485, 9142])).
% 2.50/2.44 tff(14502,plain,((~trans(s104, s32)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14503,plain,
% 2.50/2.44 (~trans(s104, s32)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14502, 13586])).
% 2.50/2.44 tff(14504,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s24) | (~trans(s104, s24)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s24) | (~trans(s104, s24)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14505,plain,
% 2.50/2.44 (((~trans(s104, s24)) | (~always19(s104)) | always19(s24)) <=> ((~always19(s104)) | always19(s24) | (~trans(s104, s24)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14506,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s24)) | (~always19(s104)) | always19(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s24) | (~trans(s104, s24))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14505])).
% 2.50/2.44 tff(14507,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s24)) | (~always19(s104)) | always19(s24))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s24) | (~trans(s104, s24)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14506, 14504])).
% 2.50/2.44 tff(14508,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s24)) | (~always19(s104)) | always19(s24))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14509,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s24) | (~trans(s104, s24))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14508, 14507])).
% 2.50/2.44 tff(14510,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14509, 11717, 8567, 14485, 9208])).
% 2.50/2.44 tff(14511,plain,((~trans(s104, s24)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14512,plain,
% 2.50/2.44 (~trans(s104, s24)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14511, 13586])).
% 2.50/2.44 tff(14513,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s22) | (~trans(s104, s22)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s22) | (~trans(s104, s22)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14514,plain,
% 2.50/2.44 (((~trans(s104, s22)) | (~always19(s104)) | always19(s22)) <=> ((~always19(s104)) | always19(s22) | (~trans(s104, s22)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14515,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s22)) | (~always19(s104)) | always19(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s22) | (~trans(s104, s22))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14514])).
% 2.50/2.44 tff(14516,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s22)) | (~always19(s104)) | always19(s22))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s22) | (~trans(s104, s22)))),
% 2.50/2.44 inference(transitivity,[status(thm)],[14515, 14513])).
% 2.50/2.44 tff(14517,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s22)) | (~always19(s104)) | always19(s22))),
% 2.50/2.44 inference(quant_inst,[status(thm)],[])).
% 2.50/2.44 tff(14518,plain,
% 2.50/2.44 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s22) | (~trans(s104, s22))),
% 2.50/2.44 inference(modus_ponens,[status(thm)],[14517, 14516])).
% 2.50/2.44 tff(14519,plain,
% 2.50/2.44 ($false),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14518, 11748, 8567, 14485, 9227])).
% 2.50/2.44 tff(14520,plain,((~trans(s104, s22)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.44 tff(14521,plain,
% 2.50/2.44 (~trans(s104, s22)),
% 2.50/2.44 inference(unit_resolution,[status(thm)],[14520, 13586])).
% 2.50/2.44 tff(14522,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s20) | (~trans(s104, s20)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s20) | (~trans(s104, s20)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14523,plain,
% 2.50/2.44 (((~trans(s104, s20)) | (~always19(s104)) | always19(s20)) <=> ((~always19(s104)) | always19(s20) | (~trans(s104, s20)))),
% 2.50/2.44 inference(rewrite,[status(thm)],[])).
% 2.50/2.44 tff(14524,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s20)) | (~always19(s104)) | always19(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s20) | (~trans(s104, s20))))),
% 2.50/2.44 inference(monotonicity,[status(thm)],[14523])).
% 2.50/2.44 tff(14525,plain,
% 2.50/2.44 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s20)) | (~always19(s104)) | always19(s20))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s20) | (~trans(s104, s20)))),
% 2.50/2.45 inference(transitivity,[status(thm)],[14524, 14522])).
% 2.50/2.45 tff(14526,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s20)) | (~always19(s104)) | always19(s20))),
% 2.50/2.45 inference(quant_inst,[status(thm)],[])).
% 2.50/2.45 tff(14527,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s20) | (~trans(s104, s20))),
% 2.50/2.45 inference(modus_ponens,[status(thm)],[14526, 14525])).
% 2.50/2.45 tff(14528,plain,
% 2.50/2.45 ($false),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14527, 11779, 8567, 14485, 9241])).
% 2.50/2.45 tff(14529,plain,((~trans(s104, s20)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.45 tff(14530,plain,
% 2.50/2.45 (~trans(s104, s20)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14529, 13586])).
% 2.50/2.45 tff(14531,assumption,(trans(s104, s40)), introduced(assumption)).
% 2.50/2.45 tff(14532,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s40) | (~trans(s104, s40)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s40) | (~trans(s104, s40)))),
% 2.50/2.45 inference(rewrite,[status(thm)],[])).
% 2.50/2.45 tff(14533,plain,
% 2.50/2.45 (((~trans(s104, s40)) | (~always19(s104)) | always19(s40)) <=> ((~always19(s104)) | always19(s40) | (~trans(s104, s40)))),
% 2.50/2.45 inference(rewrite,[status(thm)],[])).
% 2.50/2.45 tff(14534,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s40)) | (~always19(s104)) | always19(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s40) | (~trans(s104, s40))))),
% 2.50/2.45 inference(monotonicity,[status(thm)],[14533])).
% 2.50/2.45 tff(14535,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s40)) | (~always19(s104)) | always19(s40))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s40) | (~trans(s104, s40)))),
% 2.50/2.45 inference(transitivity,[status(thm)],[14534, 14532])).
% 2.50/2.45 tff(14536,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s40)) | (~always19(s104)) | always19(s40))),
% 2.50/2.45 inference(quant_inst,[status(thm)],[])).
% 2.50/2.45 tff(14537,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s40) | (~trans(s104, s40))),
% 2.50/2.45 inference(modus_ponens,[status(thm)],[14536, 14535])).
% 2.50/2.45 tff(14538,plain,
% 2.50/2.45 ($false),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14537, 14531, 8567, 14485, 9083])).
% 2.50/2.45 tff(14539,plain,((~trans(s104, s40)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.45 tff(14540,plain,
% 2.50/2.45 (~trans(s104, s40)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14539, 13586])).
% 2.50/2.45 tff(14541,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s4) | (~trans(s104, s4)))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s4) | (~trans(s104, s4)))),
% 2.50/2.45 inference(rewrite,[status(thm)],[])).
% 2.50/2.45 tff(14542,plain,
% 2.50/2.45 (((~trans(s104, s4)) | (~always19(s104)) | always19(s4)) <=> ((~always19(s104)) | always19(s4) | (~trans(s104, s4)))),
% 2.50/2.45 inference(rewrite,[status(thm)],[])).
% 2.50/2.45 tff(14543,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s4)) | (~always19(s104)) | always19(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~always19(s104)) | always19(s4) | (~trans(s104, s4))))),
% 2.50/2.45 inference(monotonicity,[status(thm)],[14542])).
% 2.50/2.45 tff(14544,plain,
% 2.50/2.45 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s4)) | (~always19(s104)) | always19(s4))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s4) | (~trans(s104, s4)))),
% 2.50/2.45 inference(transitivity,[status(thm)],[14543, 14541])).
% 2.50/2.45 tff(14545,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | ((~trans(s104, s4)) | (~always19(s104)) | always19(s4))),
% 2.50/2.45 inference(quant_inst,[status(thm)],[])).
% 2.50/2.45 tff(14546,plain,
% 2.50/2.45 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | (~always19(X)) | always19(Y))) | (~always19(s104)) | always19(s4) | (~trans(s104, s4))),
% 2.50/2.45 inference(modus_ponens,[status(thm)],[14545, 14544])).
% 2.50/2.45 tff(14547,plain,
% 2.50/2.45 ($false),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14546, 13243, 8567, 14485, 9373])).
% 2.50/2.45 tff(14548,plain,((~trans(s104, s4)) | (~always19(s104))), inference(lemma,lemma(discharge,[]))).
% 2.50/2.45 tff(14549,plain,
% 2.50/2.45 (~trans(s104, s4)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14548, 13586])).
% 2.50/2.45 tff(14550,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s26) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s85) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s100) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[13572, 13241, 13204, 14549, 14540, 14530, 14521, 14512, 14503, 14494])).
% 2.50/2.45 tff(14551,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s33) | trans(s104, s34) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s42) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s90) | trans(s104, s92) | trans(s104, s93) | trans(s104, s94) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14550, 14479, 14471, 14463])).
% 2.50/2.45 tff(14552,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s30) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s44) | trans(s104, s45) | trans(s104, s46) | trans(s104, s47) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s79) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s92) | trans(s104, s93) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14551, 14455, 14447, 14439, 14431])).
% 2.50/2.45 tff(14553,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s6) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s45) | trans(s104, s46) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s84) | trans(s104, s86) | trans(s104, s87) | trans(s104, s88) | trans(s104, s89) | trans(s104, s92) | trans(s104, s93) | trans(s104, s95) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14552, 14423, 14415, 14407, 14394])).
% 2.50/2.45 tff(14554,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s14) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s45) | trans(s104, s46) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s77) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s86) | trans(s104, s88) | trans(s104, s89) | trans(s104, s92) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14553, 14381, 14373, 14360, 14347])).
% 2.50/2.45 tff(14555,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s3) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s18) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s45) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s86) | trans(s104, s88) | trans(s104, s89) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s98) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.45 inference(unit_resolution,[status(thm)],[14554, 14339, 14331, 14323, 14315])).
% 2.50/2.45 tff(14556,plain,
% 2.50/2.45 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s45) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s82) | trans(s104, s83) | trans(s104, s88) | trans(s104, s89) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s101) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14555, 14307, 14299, 14291, 14278])).
% 2.50/2.46 tff(14557,plain,
% 2.50/2.46 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s11) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s36) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s41) | trans(s104, s43) | trans(s104, s48) | trans(s104, s49) | trans(s104, s50) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s83) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14556, 14270, 14262, 14254, 14246])).
% 2.50/2.46 tff(14558,plain,
% 2.50/2.46 (trans(s104, s0) | trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s43) | trans(s104, s48) | trans(s104, s49) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s83) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14557, 14238, 14225, 14217, 14209])).
% 2.50/2.46 tff(14559,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s17) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s49) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s61) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s65) | trans(s104, s66) | trans(s104, s67) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14558, 14201, 14188, 14175])).
% 2.50/2.46 tff(14560,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s8) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s49) | trans(s104, s51) | trans(s104, s52) | trans(s104, s53) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s60) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s71) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14559, 14162, 14154, 14141, 14133])).
% 2.50/2.46 tff(14561,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s49) | trans(s104, s51) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s58) | trans(s104, s59) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14560, 14125, 14112, 14104, 14096])).
% 2.50/2.46 tff(14562,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s5) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s69) | trans(s104, s70) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s75) | trans(s104, s76) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14561, 14088, 14075, 14067, 14059])).
% 2.50/2.46 tff(14563,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s27) | trans(s104, s28) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s56) | trans(s104, s57) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s78) | trans(s104, s80) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14562, 14046, 14038, 14030, 14022])).
% 2.50/2.46 tff(14564,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s12) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s21) | trans(s104, s23) | trans(s104, s25) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s57) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s73) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s93) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14563, 14009, 13996, 13988, 13980])).
% 2.50/2.46 tff(14565,plain,
% 2.50/2.46 (trans(s104, s1) | trans(s104, s2) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s25) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s57) | trans(s104, s62) | trans(s104, s63) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s99) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14564, 13972, 13964, 13956, 13948])).
% 2.50/2.46 tff(14566,plain,
% 2.50/2.46 (trans(s104, s2) | trans(s104, s7) | trans(s104, s9) | trans(s104, s10) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s29) | trans(s104, s31) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s55) | trans(s104, s57) | trans(s104, s62) | trans(s104, s64) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14565, 13940, 13932, 13919, 13906])).
% 2.50/2.46 tff(14567,plain,
% 2.50/2.46 (trans(s104, s2) | trans(s104, s9) | trans(s104, s10) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s29) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s52) | trans(s104, s54) | trans(s104, s57) | trans(s104, s62) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.46 inference(unit_resolution,[status(thm)],[14566, 13898, 13890, 13877, 13864])).
% 2.50/2.47 tff(14568,plain,
% 2.50/2.47 (trans(s104, s9) | trans(s104, s10) | trans(s104, s13) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s33) | trans(s104, s35) | trans(s104, s37) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s54) | trans(s104, s57) | trans(s104, s62) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s102) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14567, 13851, 13843, 13835])).
% 2.50/2.47 tff(14569,plain,
% 2.50/2.47 (trans(s104, s9) | trans(s104, s10) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s33) | trans(s104, s35) | trans(s104, s38) | trans(s104, s39) | trans(s104, s48) | trans(s104, s54) | trans(s104, s57) | trans(s104, s62) | trans(s104, s66) | trans(s104, s68) | trans(s104, s70) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14568, 13827, 13819, 13811])).
% 2.50/2.47 tff(14570,plain,
% 2.50/2.47 (trans(s104, s9) | trans(s104, s10) | trans(s104, s15) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s33) | trans(s104, s35) | trans(s104, s38) | trans(s104, s39) | trans(s104, s54) | trans(s104, s57) | trans(s104, s66) | trans(s104, s68) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14569, 13803, 13795, 13787])).
% 2.50/2.47 tff(14571,plain,
% 2.50/2.47 (trans(s104, s10) | trans(s104, s16) | trans(s104, s19) | trans(s104, s23) | trans(s104, s35) | trans(s104, s38) | trans(s104, s39) | trans(s104, s54) | trans(s104, s66) | trans(s104, s68) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s88) | trans(s104, s96) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14570, 13779, 13771, 13758, 13750])).
% 2.50/2.47 tff(14572,plain,
% 2.50/2.47 (trans(s104, s10) | trans(s104, s16) | trans(s104, s23) | trans(s104, s35) | trans(s104, s38) | trans(s104, s66) | trans(s104, s68) | trans(s104, s72) | trans(s104, s74) | trans(s104, s78) | trans(s104, s81) | trans(s104, s96) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14571, 13742, 13729, 13721, 13713])).
% 2.50/2.47 tff(14573,plain,
% 2.50/2.47 (trans(s104, s10) | trans(s104, s23) | trans(s104, s35) | trans(s104, s38) | trans(s104, s66) | trans(s104, s68) | trans(s104, s72) | trans(s104, s78) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14572, 13700, 13692, 13684, 13676])).
% 2.50/2.47 tff(14574,plain,
% 2.50/2.47 (trans(s104, s35) | trans(s104, s38) | trans(s104, s66) | trans(s104, s72) | trans(s104, s78) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14573, 13668, 13655, 13647])).
% 2.50/2.47 tff(14575,plain,
% 2.50/2.47 (trans(s104, s38) | trans(s104, s78) | trans(s104, s97) | trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14574, 13639, 13631, 13618])).
% 2.50/2.47 tff(14576,plain,
% 2.50/2.47 (trans(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14575, 13610, 13602, 13594])).
% 2.50/2.47 tff(14577,plain,
% 2.50/2.47 (((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s104, s103)) | node14(s104, s103))) <=> ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s104, s103)) | node14(s104, s103))),
% 2.50/2.47 inference(rewrite,[status(thm)],[])).
% 2.50/2.47 tff(14578,plain,
% 2.50/2.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | ((~trans(s104, s103)) | node14(s104, s103))),
% 2.50/2.47 inference(quant_inst,[status(thm)],[])).
% 2.50/2.47 tff(14579,plain,
% 2.50/2.47 ((~![Y: $i, X: $i] : ((~trans(X, Y)) | node14(X, Y))) | (~trans(s104, s103)) | node14(s104, s103)),
% 2.50/2.47 inference(modus_ponens,[status(thm)],[14578, 14577])).
% 2.50/2.47 tff(14580,plain,
% 2.50/2.47 (node14(s104, s103)),
% 2.50/2.47 inference(unit_resolution,[status(thm)],[14579, 14576, 7])).
% 2.50/2.47 tff(14581,plain,
% 2.50/2.48 (((~![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(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103)))) <=> ((~![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(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103)))),
% 2.50/2.48 inference(rewrite,[status(thm)],[])).
% 2.50/2.48 tff(14582,plain,
% 2.50/2.48 (((~m_main_v_state2(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s103)) | m_main_v_state2(s103, c_n2)) <=> (m_main_v_state2(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103)))),
% 2.50/2.48 inference(rewrite,[status(thm)],[])).
% 2.50/2.48 tff(14583,plain,
% 2.50/2.48 (((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s103)) | m_main_v_state2(s103, 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(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103))))),
% 2.50/2.48 inference(monotonicity,[status(thm)],[14582])).
% 2.50/2.48 tff(14584,plain,
% 2.50/2.48 (((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s103)) | m_main_v_state2(s103, 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(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103)))),
% 2.50/2.48 inference(transitivity,[status(thm)],[14583, 14581])).
% 2.50/2.48 tff(14585,plain,
% 2.50/2.48 ((~![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(s104, c_c2)) | node9(s104) | node8(s104) | node10(s104) | node11(s104) | node12(s104) | (~node14(s104, s103)) | m_main_v_state2(s103, c_n2))),
% 2.50/2.48 inference(quant_inst,[status(thm)],[])).
% 2.50/2.48 tff(14586,plain,
% 2.50/2.48 ((~![Y: $i, X: $i] : ((~m_main_v_state2(X, c_c2)) | node9(X) | node8(X) | node10(X) | node11(X) | node12(X) | (~node14(X, Y)) | m_main_v_state2(Y, c_n2))) | m_main_v_state2(s103, c_n2) | node10(s104) | node11(s104) | node9(s104) | (~m_main_v_state2(s104, c_c2)) | node12(s104) | node8(s104) | (~node14(s104, s103))),
% 2.50/2.48 inference(modus_ponens,[status(thm)],[14585, 14584])).
% 2.50/2.48 tff(14587,plain,
% 2.50/2.48 ($false),
% 2.50/2.48 inference(unit_resolution,[status(thm)],[14586, 726, 13112, 13144, 13192, 13184, 13180, 13163, 13155, 14580])).
% 2.50/2.48 % SZS output end Proof
%------------------------------------------------------------------------------